System and method for multi-parameter spectroscopy

ABSTRACT

An apparatus for detecting a material within a sample includes a light emitting unit for directing at least one light beam through the sample. A plurality of units receive the light beam that has passed through the sample and performs a spectroscopic analysis of the sample based on the received light beam. Each of the plurality of units analyze a different parameter with respect to the sample a provide a separate output signal with respect to the analysis. A processor detects the material with respect each of the provided separate output signals.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation of U.S. patent application Ser. No.15/405,974, filed Jan. 13, 2017 and entitled SYSTEM AND METHOD FORMULTI-PARAMETER SPECTROSCOPY, which U.S. patent application Ser. No.15/405,974 claims the benefit of U.S. Provisional Application No.62/278,186, filed Jan. 13, 2016 and entitled MULTI-PARAMETERSPECTROSCOPY, and claims the benefit of U.S. Provisional Application No.62/322,507, filed Apr. 14, 2016 and entitled RAMAN SPECTROSCOPY WITHORBITAL ANGULAR MOMENTUM, and claims the benefit of U.S. ProvisionalApplication No. 62/365,486, filed Jul. 22, 2016 and entitledINCE-GAUSSIAN SPECTROSCOPY, each of which is incorporated by referenceherein in its entirety.

U.S. patent application Ser. No. 15/405,974 is also aContinuation-in-Part of U.S. application Ser. No. 14/875,507 filed Oct.5, 2015 and entitled SYSTEM AND METHOD FOR EARLY DETECTION OF ALZHEIMERSBY DETECTING AMYLOID-BETA USING ORBITAL ANGULAR MOMENTUM, now U.S. Pat.No. 9,784,724 issued Oct. 10, 2017, and it is also aContinuation-in-Part of U.S. application Ser. No. 15/348,608 filed Nov.10, 2016 and entitled SYSTEM AND METHOD USING OAM SPECTROSCOPYLEVERAGING FRACTIONAL ORBITAL ANGULAR MOMENTUM AS SIGNATURE TO DETECTMATERIALS, now U.S. Pat. No. 9,645,083 issued May 9, 2017, and it isalso a Continuation-in-Part of U.S. application Ser. No. 15/049,594filed Feb. 22, 2016 and entitled SYSTEM AND METHOD FOR MAKINGCONCENTRATION MEASUREMENTS WITHIN A SAMPLE MATERIAL USING ORBITALANGULAR MOMENTUM, now U.S. Pat. No. 9,714,902 issued Jul. 25, 2017. U.S.application Ser. Nos. 14/875,507; 15/348,608; 15/049,594; and U.S. Pat.Nos. 9,784,724; 9,645,083; and 9,714,902 are incorporated by referenceherein in their entirety.

TECHNICAL FIELD

The present invention relates to the detection of materials within asample, and more particularly, to the detection of materials within asample based multi-parameter spectroscopy.

BACKGROUND

Concentration measurements and detection of the presence of organic andnon-organic materials is of great interest in a number of applications.In one example, detection of materials within human tissue is anincreasingly important aspect of healthcare for individuals. Thedevelopment of non-invasive measurement techniques for monitoringbiological and metabolic agents within human tissue is an importantaspect of diagnosis therapy of various human diseases and may play a keyrole in the proper management of diseases. The development ofnon-invasive measurement techniques for monitoring biological andmetabolic agents within human tissue is an important aspect of diagnosistherapy of various human diseases and may play a key role in the propermanagement of diseases. One such material relevant to Alzheimer's isamyloid-beta. Thus, there is a need for an improved manner ofamyloid-beta detection to better improve detection of early stages ofAlzheimer's.

Another example of a biological agent that may be monitored for withinhuman tissue is glucose. Glucose (C₆H₁₂O₆) is a monosaccharide sugar andis one of the most important carbohydrate nutrient sources. Glucose isfundamental to almost all biological processes and is required for theproduction of ATP adenosine triphosphate and other essential cellularcomponents. The normal range of glucose concentration within human bloodis 70-160 mg/dl depending on the time of the last meal, the extent ofphysical tolerance and other factors. Freely circulating glucosemolecules stimulate the release of insulin from the pancreas. Insulinhelps glucose molecules to penetrate the cell wall by binding twospecific receptors within cell membranes which are normally impermeableto glucose.

One disease associated with issues related to glucose concentrations isdiabetes. Diabetes is a disorder caused by the decreased production ofinsulin, or by a decreased ability to utilize insulin and transport theglucose across cell membranes. As a result, a high potentially dangerousconcentration of glucose can accumulate within the blood (hyperglycemia)during the disease. Therefore, it is of great importance to maintainblood glucose concentration within a normal range in order to preventpossible severe physiological complications.

One significant role of physiological glucose monitoring is thediagnosis and management of several metabolic diseases, such as diabetesmellitus (or simply diabetes). There are a number of invasive andnon-invasive techniques presently used for glucose monitoring. Theproblem with existing non-invasive glucose monitoring techniques is thata clinically acceptable process has not yet been determined. Standardtechniques from the analysis of blood currently involve an individualpuncturing a finger and subsequent analysis of collected blood samplesfrom the finger. In recent decades, non-invasive blood glucosemonitoring has become an increasingly important topic of investigationin the realm of biomedical engineering. In particular, the introductionof optical approaches has caused some advances within the field.Advances in optics have led to a focused interest in optical imagingtechnologies and the development of non-invasive imaging systems. Theapplication of optical methods to monitoring in cancer diagnostics andtreatment is also a growing field due to the simplicity and low risk ofoptical detection methods. In addition to the medical field, thedetection of various types of materials in a variety of otherenvironments would be readily apparent.

Many optical techniques for sensing different tissue metabolites andglucose in living tissue have been in development over the last 50years. These methods have been based upon florescent, near infrared andmid-infrared spectroscopy, Raman spectroscopy, photoacoustics, opticalcoherence tomography and other techniques. However, none of thesetechniques that have been tried have proved completely satisfactory.

Another organic component lending itself to optical materialconcentration sensing involves is human skin. The defense mechanisms ofhuman skin are based on the action of antioxidant substances such ascarotenoids, vitamins and enzymes. Beta carotene and lycopene representmore than 70% of the carotenoids in the human organism. The topical orsystematic application of beta carotene and lycopene is a generalstrategy for improving the defense system of the human body. Theevaluation and optimization of this treatment requires the measurementof the b-carotene and lycopene concentrations in human tissue,especially in the human skin as the barrier to the environment.

Thus, an improved non-invasive technique enabling the detection ofconcentrations and presence of various materials within a human body orother types of samples would have a number of applications within themedical field.

SUMMARY

The present invention, as disclosed and described herein, in one aspectthereof, comprise an apparatus for detecting a material within a sampleincludes a light emitting unit for directing at least one light beamthrough the sample. A plurality of spectroscopic units receive the lightbeam that has passed through the sample and performs a spectroscopicanalysis of the sample based on the received light beam. Each of theplurality of spectroscopic units analyze a different parameter withrespect to the sample, provide a separate output signal with respect tothe analysis. A processor detects the material with respect each of theprovided separate output signals.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding, reference is now made to thefollowing description taken in conjunction with the accompanyingdrawings in which:

FIG. 1 illustrates the manner for using an Orbital Angular Momentumsignature to detect the presence of a material within a sample;

FIG. 2 illustrates the manner in which an OAM generator generates an OAMtwisted beam;

FIG. 3 illustrates a light beam having orbital angular momentum impartedthereto;

FIG. 4 illustrates a series of parallel wavefronts;

FIG. 5 illustrates a wavefront having a Poynting vector spiraling arounda direction of propagation of the wavefront;

FIG. 6 illustrates a plane wavefront;

FIG. 7 illustrates a helical wavefront;

FIG. 8 illustrates a plane wave having only variations in the spinvector;

FIG. 9 illustrates the application of a unique orbital angular momentumto a wave;

FIGS. 10A-10C illustrate the differences between signals havingdifferent orbital angular momentum applied thereto;

FIG. 11A illustrates the propagation of Poynting vectors for variouseigenmodes;

FIG. 11B illustrates a spiral phase plate;

FIG. 12 illustrates a block diagram of an apparatus for providingconcentration measurements and presence detection of various materialsusing orbital angular momentum;

FIG. 13 illustrates an emitter of the system of FIG. 11;

FIG. 14 illustrates a fixed orbital angular momentum generator of thesystem of FIG. 11;

FIGS. 15A-15D illustrate various holograms for use in applying anorbital angular momentum to a plane wave signal;

FIG. 16 illustrates the relationship between Hermite-Gaussian modes andLaguerre-Gaussian modes;

FIG. 17 illustrates super-imposed holograms for applying orbital angularmomentum to a signal;

FIG. 18 illustrates a tunable orbital angular momentum generator for usein the system of FIG. 11;

FIG. 19 illustrates a block diagram of a tunable orbital angularmomentum generator including multiple hologram images therein;

FIG. 20 illustrates the manner in which the output of the OAM generatormay be varied by applying different orbital angular momentums thereto;

FIG. 21 illustrates an alternative manner in which the OAM generator mayconvert a Hermite-Gaussian beam to a Laguerre-Gaussian beam;

FIG. 22 illustrates the manner in which holograms within an OAMgenerator may twist a beam of light;

FIG. 23 illustrates the manner in which a sample receives an OAM twistedwave and provides an output wave having a particular OAM signature;

FIG. 24 illustrates the manner in which orbital angular momentuminteracts with a molecule around its beam axis;

FIG. 25 illustrates a block diagram of the matching circuitry foramplifying a received orbital angular momentum signal;

FIG. 26 illustrates the manner in which the matching module may usenon-linear crystals in order to generate a higher order orbital angularmomentum light beam;

FIG. 27 illustrates a block diagram of an orbital angular momentumdetector and user interface;

FIG. 28 illustrates the effect of sample concentrations upon the spinangular polarization and orbital angular polarization of a light beampassing through a sample;

FIG. 29 more particularly illustrates the process that alters theorbital angular momentum polarization of a light beam passing through asample;

FIG. 30 provides a block diagram of a user interface of the system ofFIG. 12;

FIG. 31 illustrates a network configuration for passing around datacollected via devices such as that illustrated in FIG. 15;

FIG. 32 provides a block diagram of a more particular embodiment of anapparatus for measuring the concentration and presence of glucose usingorbital angular momentum;

FIG. 33 illustrates an optical system for detecting a unique OAMsignature of a signal passing through a sample under test;

FIG. 34 illustrates the manner in which the ellipticity of an OAMintensity diagram changes after passing through a sample;

FIG. 35 illustrates the manner in which a center of gravity of anintensity diagram shifts after passing through a sample;

FIG. 36 illustrates the manner in which an axis of the intensity diagramshifts after passing through a sample;

FIG. 37A illustrates an OAM signature of a sample consisting only ofwater;

FIG. 37B illustrates an OAM signature of a sample of 15% glucose inwater;

FIG. 38A illustrates an interferogram of a sample consisting only ofwater;

FIG. 38B illustrates an interferogram of a sample of 15% glucose inwater;

FIG. 39 shows the amplitude of an OAM beam;

FIG. 40 shows the phase of an OAM beam;

FIG. 41 is a chart illustrating the ellipticity of a beam on the outputof a Cuvette for three different OAM modes;

FIGS. 42A-42C illustrates the propagation due to and annulus shaped beamfor a Cuvette, water and glucose;

FIG. 43 illustrates OAM propagation through water for differing drivevoltages;

FIG. 44 illustrates an example of a light beam that is altered by ahologram to produce an OAM twisted beam;

FIG. 45 illustrates various OAM modes produced by a spatial lightmodulator;

FIG. 46 illustrates an ellipse;

FIG. 47 is a flow diagram illustrating a process for analyzing intensityimages;

FIG. 48 illustrates an ellipse fitting algorithm;

FIG. 49 illustrates the generation of fractional orthogonal states;

FIG. 50 illustrates the use of a spatial light modulator for thegeneration of fractional OAM beams;

FIG. 51 illustrates one manner for the generation of fractional OAM beamusing superimposed Laguerre Gaussian beams;

FIG. 52 illustrates the decomposition of a fractional OAM beam intointeger OAM states;

FIG. 53 illustrates the manner in which a spatial light modulator maygenerate a hologram for providing fractional OAM beams;

FIG. 54 illustrates the generation of a hologram to produce non-integerOAM beams;

FIG. 55 is a flow diagram illustrating the generation of a hologram forproducing non-integer OAM beams;

FIG. 56 illustrates the intensity and phase profiles for noninteger OAMbeams;

FIG. 57 is a block diagram illustrating fractional OAM beams for OAMspectroscopy analysis;

FIG. 58 illustrates an example of an OAM state profile;

FIG. 59 illustrates the manner for combining multiple variedspectroscopy techniques to provide multiparameter spectroscopy analysis;

FIG. 60 illustrates a schematic drawing of a spec parameter for makingrelative measurements in an optical spectrum;

FIG. 61 illustrates an electromagnetic spectrum;

FIG. 62 illustrates the infrared spectrum of water vapor;

FIG. 63 illustrates the stretching and bending vibrational modes ofwater;

FIG. 64 illustrates the stretching and bending vibrational modes forCO₂;

FIG. 65 illustrates the infrared spectrum of carbon dioxide;

FIG. 66 illustrates the energy of an anharmonic oscillator as a functionof the interatomic distance;

FIG. 67 illustrates the energy curve for a vibrating spring andquantized energy level;

FIG. 68 illustrates Rayleigh scattering and Ramen scattering by Stokesand anti-Stokes resonance;

FIG. 69 illustrates circuits for carrying out polarized Rahmantechniques;

FIG. 70 illustrates circuitry for combining polarized and non-polarizedRahman spectroscopy;

FIG. 71 illustrates a combination of polarized and non-polarized Rahmanspectroscopy with optical vortices;

FIG. 72 illustrates the electromagnetic wave attenuation by atmosphericwater versus frequency and wavelength;

FIG. 73 illustrates the absorption and emission sequences associatedwith fluorescence spectroscopy;

FIG. 74A illustrates the absorption spectra of various materials;

FIG. 74B illustrates the fluorescence spectra of various materials;

FIG. 75 illustrates a pump-probe spectroscopy set up;

FIG. 76 illustrates an enhanced Ramen signal;

FIG. 77 illustrates a pump-probe OAM spectroscopy set up;

FIG. 78 illustrates measured eccentricities of OAM beams;

FIG. 79 illustrates a combination of OAM spectroscopy with Ramenspectroscopy for the generation of differential signals;

FIG. 80 illustrates a flow diagram of an alignment procedure

FIG. 81 illustrates a balanced detection scheme;

FIG. 82 illustrates an elliptical coordinate system;

FIG. 83 illustrates a tracing the lips with constant

FIG. 84 illustrates tracing hyperbolas with constant

FIGS. 85A and 85B illustrates even Ince Polynomials;

FIG. 86 illustrates modes and phases for even Ince mode;

FIGS. 87A and 87B illustrates odd Ince Polynomials;

FIG. 88 illustrates modes and phases for odd Ince mode;

FIG. 89 illustrates dual comp spectroscopy; and

FIG. 90 illustrates a wearable multi-parameter spectroscopy device.

DETAILED DESCRIPTION

Referring now to the drawings, wherein like reference numbers are usedherein to designate like elements throughout, the various views andembodiments of a system and method for detecting materials using orbitalangular momentum signatures are illustrated and described, and otherpossible embodiments are described. The figures are not necessarilydrawn to scale, and in some instances the drawings have been exaggeratedand/or simplified in places for illustrative purposes only. One ofordinary skill in the art will appreciate the many possible applicationsand variations based on the following examples of possible embodiments.

Referring now to the drawings, and more particularly to FIG. 1, there isillustrated the manner for detecting the presence of a particularmaterial within a sample based upon the unique orbital angular momentumsignature imparted to a signal passing through the sample. An opticalsignal 102 having a series of plane waves therein is applied to a devicefor applying an orbital angular momentum (OAM) signal to the opticalsignal 102 such as a spatial light modulator (SLM) 104. While thepresent embodiment envisions the use of an optical signal 102, othertypes of signals having orbital angular momentum or other orthogonalsignals therein may be utilized in alternative embodiments. The SLM 104generates an output signal 106 having a known OAM twist applied to thesignal. The OAM twist has known characteristics that act as a baselineprior to the application of the output signal 106 to a sample 108. Thesample 108 may comprise a material contained within a holding container,such as a cuvette, or may be a material in its natural state, such asthe eye or body of a patient or its naturally occurring location innature. The sample 108 only indicates that a particular material or itemof interest is being detected by the describe system. While passingthrough the sample 108, the output signal 106 has a unique OAM signatureapplied thereto that is provided as an OAM distinct signature signal110. OAM beams have been observed to exhibit unique topologicalevolution upon interacting with chiral solutions. While it has been seenthat chiral molecules create unique OAM signatures when an OAM beam ispassed through a sample of the chiral material, the generation of uniqueOAM signatures from signals passing through non-chiralmolecules/material may also be provided. Given these unique topologicalfeatures one can detect the existence of a molecule in a given solutionwith specific signatures in both the amplitude and phase measurements.This distinct signature signal 110 may then be examined using forexample a camera 112 in order to detect the unique signalcharacteristics applied thereto and determine the material within thesample based upon this unique signature. Application of multi-parameterspectroscopy for the detection of different molecules can be applied todifferent industries including, but not limited to, food (identificationof food spoilage), Nanoscale Material development for defense andnational security, chemical industries, pharma and medical industriesfor testing where non-invasive solutions are critical, medical anddental industry for identification of infections, cancer cells, organiccompounds and many others. The determination of the particular materialindicated by the unique signature may be determined in one embodiment bycomparison of the signature to a unique database of signatures thatinclude known signatures that are associated with a particular materialor concentration. The manner of creating such a database would be knownto one skilled in the art.

Referring now to FIG. 2 illustrates the manner in which an OAM generator220 may generate an OAM twisted beam 222. The OAM generator 210 may useany number of devices to generate the twisted beam 222 includingholograms with an amplitude mask, holograms with a phase mask, SpatialLight Modulators (SLMs) or Digital Light Processors (DLPs). The OAMgenerator 220 receives a light beam 221 (for example from a laser) thatincludes a series of plane waves. The OAM generator 220 applies anorbital angular momentum to the beam 222. The beam 222 includes a singleOAM mode as illustrated by the intensity diagram 223. The OAM twistedbeam 222 is passed through a sample 224 including material that is beingdetected. As mentioned previously the sample 224 may be in a containeror its naturally occurring location. The presence of the material withinthe sample 224 will create new OAM mode levels within the intensitydiagram 225. Once the beam 222 passes through the sample 224, the outputbeam 226 will have three distinct signatures associated therewith basedon a detection of a particular material at a particular concentration.These signatures include a change in eccentricity 228 of the intensitypattern, a shift or translation 230 in the center of gravity of theintensity pattern and a rotation 232 in three general directions (α, β,γ) of the ellipsoidal intensity pattern output. Each of these distinctsignature indications may occur in any configuration and each distinctsignature will provide a unique indication of the presence of particularmaterials and the concentrations of these detected materials. Thesethree distinct signatures will appear when a molecule under measurementis detected and the manner of change of these signatures representsconcentration levels. The detection of the helicity spectrums from thebeam passing through the sample 224 involves detecting the helical wavescatters (forward and backward) from the sample material.

The use of the OAM of light for the metrology of glucose, amyloid betaand other chiral materials has been demonstrated using theabove-described configurations. OAM beams are observed to exhibit uniquetopological evolution upon interacting with chiral solutions within 3 cmoptical path links. It should be realized that unique topologicalevolution may also be provided from non-chiral materials. Chiralsolution, such as Amyloid-beta, glucose and others, have been observedto cause orbital angular momentum (OAM) beams to exhibit uniquetopological evolution when interacting therewith. OAM is not typicallycarried by naturally scattered photons which make use of the twistedbeams more accurate when identifying the helicities of chiral moleculesbecause OAM does not have ambient light scattering (noise) in itsdetection. Thus, the unique OAM signatures imparted by a material is notinterfered with by ambient light scattering (noise) that does not carryOAM in naturally scattered photons making detection much more accurate.Given these unique topological features one can detect the amyloid-betapresence and concentration within a given sample based upon a specificsignature in both amplitude and phase measurements. Molecular chiralitysignifies a structural handedness associated with variance under spatialinversion or a combination of inversion and rotation, equivalent to theusual criteria of a lack of any proper axes of rotation. Something ischiral when something cannot be made identical to its reflection. Chiralmolecules that are not superimposable on their mirror image are known asEnantiomers. Traditionally, engages circularly polarized light, even inthe case of optical rotation, interpretation of the phenomenon commonlyrequires the plane polarized state to be understood as a superpositionof circular polarizations with opposite handedness. For circularlypolarized light, the left and right forms designate the sign ofintrinsic spin angular momentum, ±h and also the helicity of the locusdescribed by the associated electromagnetic field vectors. For thisreason its interactions with matter are enantiomerically specific.

The continuous symmetry measure (CSM) is used to evaluate the degree ofsymmetry of a molecule, or the chirality. This value ranges from 0 to100. The higher the symmetry value of a molecule the more symmetrydistorted the molecule and the more chiral the molecule. The measurementis based on the minimal distance between the chiral molecule and thenearest achiral molecule.

The continuous symmetry measure may be achieved according to theequation:

${S(G)} =  {100 \times \min\frac{1}{{Nd}^{2}}\sum\limits_{k = 1}^{N}}\; \middle| {Q_{k} - {\hat{Q}}_{k}} |^{2}$Q_(k): The original structure{circumflex over (Q)}_(k): The symmetry-operated structureN: Number of verticesd: Size normalization factor*The scale is 0-1 (0-100):The larger S(G) is, the higher is the deviation from G-symmetry

SG as a continuous chirality measure may be determined according to:

${S(G)} =  {100 \times \min\frac{1}{{Nd}^{2}}\sum\limits_{k = 1}^{N}}\; \middle| {Q_{k} - {\hat{Q}}_{k}} |^{2}$G: The achiral symmetry point group which minimizes S(G)Achiral molecule: S(G)=0

An achiral molecule has a value of S(G)=0. The more chiral a molecule isthe higher the value of S(G).

The considerable interest in orbital angular momentum has been enhancedthrough realization of the possibility to engineer optical vortices.Here, helicity is present in the wave-front surface of theelectromagnetic fields and the associated angular momentum is termed“orbital”. The radiation itself is commonly referred to as a ‘twisted’or ‘helical’ beam. Mostly, optical vortices have been studied only intheir interactions with achiral matter—the only apparent exception issome recent work on liquid crystals. It is timely and of interest toassess what new features, if any, can be expected if such beams are usedto interrogate any system whose optical response is associated withenantiomerically specific molecules.

First the criteria for manifestations of chirality in opticalinteractions are constructed in generalized form. For simplicity,materials with a unique enantiomeric specificity are assumed—signifyinga chirality that is intrinsic and common to all molecular components (orchromophores) involved in the optical response. Results for systems ofthis kind will also apply to single molecule studies. Longer rangetranslation/rotation order can also produce chirality, as for example intwisted nematic crystals, but such mesoscopic chirality cannot directlyengender enantiomerically specific interactions. The only exception iswhere optical waves probe two or more electronically distinct,dissymmetrically oriented but intrinsically achiral molecules orchromophores.

Chiroptical interactions can be distinguished by their electromagneticorigins: for molecular systems in their usual singlet electronic groundstate, they involve the spatial variation of the electric and magneticfields associated with the input of optical radiation. This variationover space can be understood to engage chirality either through itscoupling with di-symmetrically placed, neighboring chromophore groups(Kirkwood's two-group model, of limited application) or more generallythrough the coupling of its associated electric and magnetic fields withindividual groups. As chirality signifies a local breaking of parity itpermits an interference of electric and magnetic interactions. Even inthe two group case, the paired electric interactions of the systemcorrespond to electric and magnetic interactions of the single entitywhich the two groups comprise. Thus, for convenience, the term ‘chiralcenter’ is used in the following to denote either chromophore ormolecule.

With the advent of the laser, the Gaussian beam solution to the waveequation came into common engineering parlance, and its extension twohigher order laser modes, Hermite Gaussian for Cartesian symmetry;Laguerre Gaussian for cylindrical symmetry, etc., entered laboratoryoptics operations. Higher order Laguerre Gaussian beam modes exhibitspiral, or helical phase fronts. Thus, the propagation vector, or theeikonal of the beam, and hence the beams momentum, includes in additionto a spin angular momentum, an orbital angular momentum, i.e. a wobblearound the sea axis. This phenomenon is often referred to as vorticity.The expression for a Laguerre Gaussian beam is given in cylindricalcoordinates:

${u( {r,\theta,z} )} = {\sqrt{\frac{2{pl}}{1 + {\delta_{0,m}{{\pi( {m + \rho} )}!}}}}\frac{1}{w(z)}{\exp\lbrack {{j( {{2p} + m + 1} )}( {{\psi(z)} - \psi_{0}} )} \rbrack}( \frac{\sqrt{2}r}{w(z)} ){L_{p}^{m}( \frac{2r^{2}}{{w(z)}^{2}} )}{\exp\lbrack {{{- {jk}}\frac{r^{2}}{2{q(z)}}} + {{im}\;\theta}} \rbrack}}$

Here, w (x) is the beam spot size, q(c) is the complex beam parametercomprising the evolution of the spherical wave front and the spot size.Integers p and m are the radial and azimuthal modes, respectively. Theexp(imθ) term describes the spiral phase fronts.

Referring now also to FIG. 3, there is illustrated one embodiment of abeam for use with the system. A light beam 300 consists of a stream ofphotons 302 within the light beam 300. Each photon has an energy ±hGDand a linear momentum of ±hk which is directed along the light beam axis304 perpendicular to the wavefront. Independent of the frequency, eachphoton 302 within the light beam has a spin angular momentum 306 of ±haligned parallel or antiparallel to the direction of light beampropagation. Alignment of all of the photons 302 spins gives rise to acircularly polarized light beam. In addition to the circularpolarization, the light beams also may carry an orbital angular momentum308 which does not depend on the circular polarization and thus is notrelated to photon spin.

Lasers are widely used in optical experiments as the source ofwell-behaved light beams of a defined frequency. A laser may be used forproviding the light beam 300. The energy flux in any light beam 300 isgiven by the Poynting vector which may be calculated from the vectorproduct of the electric and magnetic fields within the light beam. In avacuum or any isotropic material, the Poynting vector is parallel to thewave vector and perpendicular to the wavefront of the light beam. In anormal laser light, the wavefronts 400 are parallel as illustrated inFIG. 4. The wave vector and linear momentum of the photons are directedalong the axis in a z direction 402. The field distributions of suchlight beams are paraxial solutions to Maxwell's wave equation butalthough these simple beams are the most common, other possibilitiesexist.

For example, beams that have 1 intertwined helical fronts are alsosolutions of the wave equation. The structure of these complicated beamsis difficult to visualize, but their form is familiar from the l=3fusilli pasta. Most importantly, the wavefront has a Poynting vector anda wave vector that spirals around the light beam axis direction ofpropagation as illustrated in FIG. 5 at 502.

A Poynting vector has an azimuthal component on the wave front and anon-zero resultant when integrated over the beam cross-section. The spinangular momentum of circularly polarized light may be interpreted in asimilar way. A beam with a circularly polarized planer wave front, eventhough it has no orbital angular momentum, has an azimuthal component ofthe Poynting vector proportional to the radial intensity gradient. Thisintegrates over the cross-section of the light beam to a finite value.When the beam is linearly polarized, there is no azimuthal component tothe Poynting vector and thus no spin angular momentum.

Thus, the momentum of each photon 302 within the light beam 300 has anazimuthal component. A detailed calculation of the momentum involves allof the electric fields and magnetic fields within the light beam,particularly those electric and magnetic fields in the direction ofpropagation of the beam. For points within the beam, the ratio betweenthe azimuthal components and the z components of the momentum is foundto be 1/kr. (where 1=the helicity or orbital angular momentum; k=wavenumber 2π/λ; r=the radius vector.) The linear momentum of each photon302 within the light beam 300 is given by hk, so if we take the crossproduct of the azimuthal component within a radius vector, r, we obtainan orbital momentum for a photon 602 of lℏ. Note also that the azimuthalcomponent of the wave vectors is 1/r and independent of the wavelength.

Referring now to FIGS. 6 and 7, there are illustrated plane wavefrontsand helical wavefronts. Ordinarily, laser beams with plane wavefronts602 are characterized in terms of Hermite-Gaussian modes. These modeshave a rectangular symmetry and are described by two mode indices m 604and n 606. There are m nodes in the x direction and n nodes in the ydirection. Together, the combined modes in the x and y direction arelabeled HGmn 608. In contrast, as shown in FIG. 7, beams with helicalwavefronts 702 are best characterized in terms of Laguerre-Gaussianmodes which are described by indices I 703, the number of intertwinedhelices 704, and p, the number of radial nodes 706. TheLaguerre-Gaussian modes are labeled LGmn 710. For 1≠0, the phasesingularity on a light beam 300 results in 0 on axis intensity. When alight beam 300 with a helical wavefront is also circularly polarized,the angular momentum has orbital and spin components, and the totalangular momentum of the light beam is (l±ℏ) per photon.

Using the orbital angular momentum state of the transmitted energysignals, physical information can be embedded within the electromagneticradiation transmitted by the signals. The Maxwell-Heaviside equationscan be represented as:

${\nabla{\cdot E}} = \frac{\rho}{ɛ_{0}}$${\nabla{\times E}} = {- \frac{\partial B}{\partial t}}$ ∇⋅B = 0${\nabla{\times B}} = {{ɛ_{0}\mu_{0}\frac{\partial E}{\partial t}} + {\mu_{0}{j( {t,x} )}{the}}}$where ∇ is the del operator, E is the electric field intensity and B isthe magnetic flux density. Using these equations, we can derive 23symmetries/conserve quantities from Maxwell's original equations.However, there are only ten well-known conserve quantities and only afew of these are commercially used. Historically if Maxwell's equationswhere kept in their original quaternion forms, it would have been easierto see the symmetries/conserved quantities, but when they were modifiedto their present vectorial form by Heaviside, it became more difficultto see such inherent symmetries in Maxwell's equations.

The conserved quantities and the electromagnetic field can berepresented according to the conservation of system energy and theconservation of system linear momentum. Time symmetry, i.e. theconservation of system energy can be represented using Poynting'stheorem according to the equations:

$H = {{\sum\limits_{i}{m_{i}\gamma_{i}c^{2}}} + {\frac{ɛ_{0}}{2}{\int{d^{3}{x( | E \middle| {}_{2}{+ c^{2}} \middle| B |^{2} )}}}}}$${\frac{{dU}^{mech}}{dt} + \frac{{dU}^{em}}{dt} + {\oint_{s^{\prime}}{d^{2}x^{\prime}{{\hat{n}}^{\prime} \cdot S}}}} = 0$

The space symmetry, i.e., the conservation of system linear momentumrepresenting the electromagnetic Doppler shift can be represented by theequations:

$P = {{\sum\limits_{i}{m_{i}\gamma_{i}v_{i}}} + {ɛ_{0}{\int{d^{3}{x( {E \times B} )}}}}}$${\frac{{dp}^{mech}}{dt} + \frac{{dp}^{em}}{dt} + {\oint_{s^{\prime}}{d^{2}x^{\prime}{n^{\hat{\prime}} \cdot T}}}} = 0$

The conservation of system center of energy is represented by theequation:

$R = {{\frac{1}{H}{\sum\limits_{i}{( {x_{i} - x_{0}} )m_{i}\gamma_{i}c^{2}}}} + {\frac{ɛ_{0}}{2H}{\int{d^{3}{x( {x - x_{0}} )}( | E^{2} \middle| {+ c^{2}} \middle| B^{2} | )}}}}$

Similarly, the conservation of system angular momentum, which gives riseto the azimuthal Doppler shift is represented by the equation:

${\frac{{dJ}^{mech}}{dt} + \frac{{dJ}^{em}}{dt} + {\oint_{s^{\prime}}{d^{2}x^{\prime}{n^{\hat{\prime}} \cdot M}}}} = 0$

For radiation beams in free space, the EM field angular momentum Jem canbe separated into two parts:J ^(em)=ε₀∫_(V′) d ³ x′(E×A)+ε₀∫_(V′) d ³ x′E _(i)[(x′−x ₀)×∇]A _(i)

For each singular Fourier mode in real valued representation:

$J^{em} = {{{- i}\frac{ɛ_{0}}{2\omega}{\int_{V^{\prime}}{d^{3}{x^{\prime}( {E^{*} \times E} )}}}} - {i\frac{ɛ_{0}}{2\omega}{\int_{V^{\prime}}{d^{3}x^{\prime}{E_{i}\lbrack {( {x^{\prime} - x_{0}} ) \times \nabla} \rbrack}E_{i}}}}}$

The first part is the EM spin angular momentum Sem, its classicalmanifestation is wave polarization. And the second part is the EMorbital angular momentum Lem its classical manifestation is wavehelicity. In general, both EM linear momentum Pem, and EM angularmomentum Jem=Lem+Sem are radiated all the way to the far field.

By using Poynting theorem, the optical vorticity of the signals may bedetermined according to the optical velocity equation:

${\frac{\partial U}{\partial t} + {\nabla{\cdot S}}} = 0$where S is the Poynting vectorS=¼(E×H*+E*×H)and U is the energy densityU=¼(ε|E| ²+μ₀ |H| ²)with E and H comprising the electric field and the magnetic field,respectively, and ε and μ₀ being the permittivity and the permeabilityof the medium, respectively. The optical vorticity V may then bedetermined by the curl of the optical velocity according to theequation:

$V = {{\nabla{\times v_{opt}}} = {\nabla{\times ( \frac{{E \times H^{*}} + {E^{*} \times H}}{ ɛ \middle| E \middle| {}_{2}{+ \mu_{0}} \middle| H |^{2}} )}}}$

Referring now to FIGS. 8 and 9, there are illustrated the manner inwhich a signal and an associated Poynting vector of the signal vary in aplane wave situation (FIG. 8) where only the spin vector is altered, andin a situation wherein the spin and orbital vectors are altered in amanner to cause the Poynting vector to spiral about the direction ofpropagation (FIG. 9).

In the plane wave situation, illustrated in FIG. 8, when only the spinvector of the plane wave is altered, the transmitted signal may take onone of three configurations. When the spin vectors are in the samedirection, a linear signal is provided as illustrated generally at 804.It should be noted that while 804 illustrates the spin vectors beingaltered only in the x direction to provide a linear signal, the spinvectors can also be altered in the y direction to provide a linearsignal that appears similar to that illustrated at 804 but in aperpendicular orientation to the signal illustrated at 804. In linearpolarization such as that illustrated at 804, the vectors for the signalare in the same direction and have a same magnitude.

Within a circular polarization as illustrated at 806, the signal vectors812 are 90 degrees to each other but have the same magnitude. Thiscauses the signal to propagate as illustrated at 806 and provide thecircular polarization 814 illustrated in FIG. 8. Within an ellipticalpolarization 808, the signal vectors 816 are also 90 degrees to eachother but have differing magnitudes. This provides the ellipticalpolarizations 818 illustrated for the signal propagation 408. For theplane waves illustrated in FIG. 8, the Poynting vector is maintained ina constant direction for the various signal configurations illustratedtherein.

The situation in FIG. 9 illustrates when a unique orbital angularmomentum is applied to a signal. When this occurs, Poynting vector S 910will spiral around the general direction of propagation 912 of thesignal. The Poynting vector 910 has three axial components Sφ, Sp and Szwhich vary causing the vector to spiral about the direction ofpropagation 912 of the signal. The changing values of the variousvectors comprising the Poynting vector 910 may cause the spiral of thePoynting vector to be varied in order to enable signals to betransmitted on a same wavelength or frequency as will be more fullydescribed herein. Additionally, the values of the orbital angularmomentum indicated by the Poynting vector 910 may be measured todetermine the presence of particular materials and the concentrationsassociated with particular materials being processed by a scanningmechanism.

FIGS. 10A-10C illustrate the differences in signals having a differenthelicity (i.e., orbital angular momentum applied thereto). The differinghelicities would be indicative of differing materials and concentrationof materials within a sample that a beam was being passed through. Bydetermining the particular orbital angular momentum signature associatedwith a signal, the particular material and concentration amounts of thematerial could be determined. Each of the spiraling Poynting vectorsassociated with a signal 1002, 1004 and 1006 provides a different-shapedsignal. Signal 1002 has an orbital angular momentum of +1, signal 1004has an orbital angular momentum of +3 and signal 1006 has an orbitalangular momentum of −4. Each signal has a distinct orbital angularmomentum and associated Poynting vector enabling the signal to beindicative of a particular material and concentration of material thatis associated with the detected orbital angular momentum. This allowsdeterminations of materials and concentrations of various types ofmaterials to be determined from a signal since the orbital angularmomentums are separately detectable and provide a unique indication ofthe particular material and the concentration of the particular materialthat has affected the orbital angular momentum of the signal transmittedthrough the sample material.

FIG. 11A illustrates the propagation of Poynting vectors for variousEigen modes. Each of the rings 1120 represents a different Eigen mode ortwist representing a different orbital angular momentum. Each of thedifferent orbital angular momentums is associated with particularmaterial and a particular concentration of the particular material.Detection of orbital angular momentums provides an indication of the apresence of an associated material and a concentration of the materialthat is being detected by the apparatus. Each of the rings 1120represents a different material and/or concentration of a selectedmaterial that is being monitored. Each of the Eigen modes has a Poyntingvector 1122 for generating the rings indicating different materials andmaterial concentrations.

Topological charge may be multiplexed to the frequency for either linearor circular polarization. In case of linear polarizations, topologicalcharge would be multiplexed on vertical and horizontal polarization. Incase of circular polarization, topological charge would multiplex onleft hand and right hand circular polarizations. The topological chargeis another name for the helicity index “I” or the amount of twist or OAMapplied to the signal. The helicity index may be positive or negative.

The topological charges 1 s can be created using Spiral Phase Plates(SPPs) as shown in FIG. 11B using a proper material with specific indexof refraction and ability to machine shop or phase mask, hologramscreated of new materials. Spiral Phase plates can transform a RF planewave (l=0) to a twisted wave of a specific helicity (i.e. l=+1).

Referring now to FIG. 12, there is illustrated a block diagram of theapparatus for providing detection of the presence of a material andconcentration measurements of various materials responsive to theorbital angular momentum detected by the apparatus in accordance withthe principles described herein above. An emitter 1202 transmits waveenergy 1204 that comprises a series of plane waves. The emitter 1202 mayprovide a series of plane waves such as those describes previously withrespect to FIG. 7. The orbital angular momentum generation circuitry1206 generates a series of waves having an orbital angular momentumapplied to the waves 1208 in a known manner. The orbital angularmomentum generation circuitry 1206 may utilize holograms or some othertype of orbital angular momentum generation process as will be morefully described herein below. The OAM generation circuitry 1206 may begenerated by transmitting plane waves through a spatial light modulator(SLM), an amplitude mask or a phase mask. The orbital angular momentumtwisted waves 1208 are applied to a sample material 1210 under test. Thesample material 1210 contains a material, and the presence andconcentration of the material is determined via a detection apparatus inaccordance with the process described herein. The sample material 1210may be located in a container or at its naturally occurring location innature such as an individual's body.

A series of output waves 1212 from the sample material 1210 exit thesample and have a particular orbital angular momentum imparted theretoas a result of the material and the concentration of the particularmaterial under study within the sample material 1210. The output waves1212 are applied to a matching module 1214 that includes a mappingaperture for amplifying a particular orbital angular momentum generatedby the specific material under study. The matching module 1214 willamplify the orbital angular momentums associated with the particularmaterial and concentration of material that is detected by theapparatus. The amplified OAM waves 1216 are provided to a detector 1218.The detector 1218 detects OAM waves relating to the material and theconcentration of a material within the sample and provides thisinformation to a user interface 1220. The detector 1218 may utilize acamera to detect distinct topological features from the beam passingthrough the sample. The user interface 1220 interprets the informationand provides relevant material type and concentration indication to anindividual or a recording device.

Referring now to FIG. 13, there is more particularly illustrated theemitter 1202. The emitter 1202 may emit a number of types of energywaves 1204 to the OAM generation module 1206. The emitter 1202 may emitoptical waves 1300, electromagnetic waves 1302, acoustic waves 1304 orany other type of particle waves 1306. The emitted waves 1204 are planewaves such as those illustrated in FIG. 4 having no orbital angularmomentum applied thereto and may come from a variety of types ofemission devices and have information included therein. In oneembodiment, the emission device may comprise a laser. Plane waves havewavefronts that are parallel to each other having no twist or helicityapplied thereto, and the orbital angular momentum of the wave is equalto 0. The Poynting vector within a plane wave is completely in line withthe direction of propagation of the wave.

The OAM generation module 1206 processes the incoming plane wave 1204and imparts a known orbital angular momentum onto the plane waves 1204provided from the emitter 1202. The OAM generation module 1206 generatestwisted or helical electromagnetic, optic, acoustic or other types ofparticle waves from the plane waves of the emitter 1202. A helical wave1208 is not aligned with the direction of propagation of the wave buthas a procession around direction of propagation as shown in FIG. 14.The OAM generation module 1206 may comprise in one embodiment a fixedorbital angular momentum generator 1402 as illustrated in FIG. 14. Thefixed orbital angular momentum generator 1402 receives the plane waves1204 from the emitter 1202 and generates an output wave 1404 having afixed orbital angular momentum applied thereto.

The fixed orbital angular momentum generator 1402 may in one embodimentcomprise a holographic image for applying the fixed orbital angularmomentum to the plane wave 1204 in order to generate the OAM twistedwave 1404. Various types of holographic images may be generated in orderto create the desired orbital angular momentum twist to an opticalsignal that is being applied to the orbital angular momentum generator1402. Various examples of these holographic images are illustrated inFIG. 15A-15D. In one embodiment, the conversion of the plane wavesignals transmitted from the emitter 1202 by the orbital angularmomentum generation circuitry 1206 may be achieved using holographicimages.

Most commercial lasers emit an HG00 (Hermite-Gaussian) mode 1602 (FIG.16) with a planar wave front and a transverse intensity described by aGaussian function. Although a number of different methods have been usedto successfully transform an HG00 Hermite-Gaussian mode 1602 into aLaguerre-Gaussian mode 1604, the simplest to understand is the use of ahologram.

The cylindrical symmetric solution upl (r,φ,z) which describesLaguerre-Gaussian beams, is given by the equation:

${u_{pl}( {r,\phi,z} )} = {{\frac{C}{( {1 + {z^{2}\text{/}z_{R}^{2}}} )^{1\text{/}2}}\lbrack \frac{r\sqrt{2}}{w(z)} \rbrack}^{l}{L_{p}^{l}\lbrack \frac{2r^{2}}{w^{2}(z)} \rbrack}{\exp\lbrack \frac{- r^{2}}{w^{2}(z)} \rbrack}{\exp\lbrack \frac{{- {ikr}^{2}}z}{2( {z^{2} + z_{R}^{2}} )} \rbrack}{\exp( {{- {il}}\;\phi} )} \times {\exp\lbrack {{i( {{2\mspace{14mu} p} + l + 1} )}\tan^{- 1}\frac{z}{z_{R}}} \rbrack}}$Where z_(R) is the Rayleigh range, w(z) is the radius of the beam, L_(P)is the Laguerre polynomial, C is a constant, and the beam waist is atz=0.

In its simplest form, a computer generated hologram is produced from thecalculated interference pattern that results when the desired beamintersects the beam of a conventional laser at a small angle. Thecalculated pattern is transferred to a high resolution holographic film.When the developed hologram is placed in the original laser beam, adiffraction pattern results. The first order of which has a desiredamplitude and phase distribution. This is one manner for implementingthe OAM generation module 1206. A number of examples of holographicimages for use within a OAM generation module are illustrated withrespect to FIGS. 15A-15D.

There are various levels of sophistication in hologram design. Hologramsthat comprise only black and white areas with no grayscale are referredto as binary holograms. Within binary holograms, the relativeintensities of the two interfering beams play no role and thetransmission of the hologram is set to be zero for a calculated phasedifference between zero and π, or unity for a phase difference between πand 2π. A limitation of binary holograms is that very little of theincident power ends up in the first order diffracted spot, although thiscan be partly overcome by blazing the grating. When mode purity is ofparticular importance, it is also possible to create more sophisticatedholograms where the contrast of the pattern is varied as a function ofradius such that the diffracted beam has the required radial profile.

A plane wave shining through the holographic images 1502 will have apredetermined orbital angular momentum shift applied thereto afterpassing through the holographic image 1502. OAM generator 1202 is fixedin the sense that a same image is used and applied to the beam beingpassed through the holographic image. Since the holographic image 1502does not change, the same orbital angular momentum is always applied tothe beam being passed through the holographic image 1502. While FIGS.15A-15D illustrate a number of embodiments of various holographic imagesthat might be utilized within the orbital angular momentum generator1202, it will be realized that any type of holographic image 1502 may beutilized in order to achieve the desired orbital angular momentum withinan beam being shined through the image 1502.

In another example of a holographic image illustrated in FIG. 17, thereis illustrated a hologram that utilizes two separate holograms that aregridded together to produce a rich number of orbital angular momentum(l). The superimposed holograms of FIG. 17 have an orbital angularmomentum of l=1 and l=3 which are superimposed upon each other tocompose the composite vortex grid 1702. The holograms utilized may alsobe built in a manner that the two holograms are gridded together toproduce a varied number of orbital angular momentums (l) not just on aline (l=+1, l=0, l=−1) but on a square which is able to identify themany variables more easily. Thus, in the example in FIG. 17, the orbitalangular momentums along the top edge vary from +4 to +1 to −2 and on thebottom edge from +2 to −1 to −4. Similarly, along the left edge theorbital angular momentums vary from +4 to +3 to +2 and on the right edgefrom −2 to −3 to −4. Across the horizontal center of the hologram theorbital angular momentums provided vary from +3 to 0 to −3 and along thevertical axis vary from +1 to 0 to −1. Thus, depending upon the portionof the grid a beam may pass through, varying orbital angular momentummay be achieved.

Referring now to FIG. 18, in addition to a fixed orbital angularmomentum generator, the orbital angular momentum generation circuitry1206 may also comprise a tunable orbital angular momentum generatorcircuitry 1802. The tunable orbital angular momentum generator 1802receives the input plane wave 1204 but additionally receives one or moretuning parameters 1804. The tuning parameters 1804 tune the tunable OAMgenerator 1802 to apply a selected orbital angular momentum so that thetuned OAM wave 1806 that is output from the OAM generator 1802 has aselected orbital angular momentum value applied thereto.

This may be achieved in any number of fashions. In one embodiment,illustrated in FIG. 22, the tunable orbital angular momentum generator1802 may include multiple hologram images 2202 within the tunable OAMgenerator 1802. The tuning parameters 1804 enable selection of one ofthe holographic images 2206 in order to provide the desired OAM wavetwisted output signal 1806 through a selector circuit 2204.Alternatively, the gridded holographic image such as that described inFIG. 16 may be utilized and the beam shined on a portion of the griddedimage to provide the desired OAM output. The tunable OAM generator 1802has the advantage of being controlled to apply a particular orbitalangular momentum to the output orbital angular momentum wave 1806depending upon the provided input parameter 1804. This enables thepresence and concentrations of a variety of different materials to bemonitored, or alternatively, for various different concentrations of thesame material to be monitored.

Referring now to FIG. 19, there is more particularly implemented a blockdiagram of a tunable orbital angular momentum generator 1802. Thegenerator 1802 includes a plurality of holographic images 1902 forproviding orbital angular momentums of various types to a provided lightsignal. These holographic images 1902 are selected responsive to aselector circuitry 1904 that is responsive to the input tuningparameters 1804. The selected filter 1906 comprises the holographicimage that has been selected responsive to the selector controller 1904and receives the input plane waves 1204 to provide the tuned orbitalangular momentum wave output 1206. In this manner, signals having adesired orbital angular momentum may be output from the OAM generationcircuitry 1206.

Referring now to FIG. 20, there is illustrated the manner in which theoutput of the OAM generator 1206 may vary a signal by applying differentorbital angular momentums thereto. FIG. 20 illustrates helical phasefronts in which the Poynting vector is no longer parallel to the beamaxis and thus has an orbital angular momentum applied thereto. In anyfixed radius within the beam, the Poynting vector follows a spiraltrajectory around the axis. Rows are labeled by l, the orbital angularmomentum quantum number, L=lh is the beams orbital angular momentum perphoton within the output signal. For each l, the left column 2002 is thelight beam's instantaneous phase. The center column 2004 comprises theangular intensity profiles and the right column 2006 illustrates whatoccurs when such a beam interferes with a plane wave and produces aspiral intensity pattern. This is illustrated for orbital angularmomentums of −1, 0, 1, 2 and 3 within the various rows of FIG. 23.

Referring now to FIG. 21, there is illustrated an alternative manner inwhich the OAM generator 1206 may convert a Hermite-Gaussian beam outputfrom an emitter 1202 to a Laguerre-Gaussian beams having impartedtherein an orbital angular momentum using mode converters 2104 and aDove prism 2110. The Hermite-Gaussian mode plane waves 2102 are providedto a π/2 mode convertor 2104. The π/2 mode convertor 2104 produce beamsin the Laguerre-Gaussian modes 2106. The Laguerre-Gaussian modes beams2106 are applied to either a it mode convertor 2108 or a dove prism 2110that reverses the mode to create a reverse Laguerre-Gaussian mode signal2112.

Referring now to FIG. 22, there is illustrated the manner in whichholograms within the OAM generator 1206 generate a twisted light beam. Ahologram 2202 can produce light beam 2204 and light beam 2206 havinghelical wave fronts and associated orbital angular momentum lh perphoton. The appropriate hologram 2202 can be calculated or generatedfrom the interference pattern between the desired beam form 2204, 2206and a plane wave 2208. The resulting holographic pattern within thehologram 2202 resembles a diffraction grating, but has a 1-prongeddislocation at the beam axis. When the hologram is illuminated with theplane wave 2208, the first-order diffracted beams 2204 and 2206 have thedesired helical wave fronts to provide the desired first ordereddiffracted beam display 2210.

Referring now to FIG. 23, there is more particularly illustrated themanner in which the sample 1210 receives the input OAM twisted wave 1208provided from the OAM generator 1206 and provides an output OAM wave1212 having a particular OAM signature associated therewith that dependsupon the material or the concentration of a particular monitoredmaterial within the sample 1210. The sample 1210 may comprise any samplethat is under study and may be in a solid form, liquid form or gas form.The sample material 1210 that may be detected using the system describedherein may comprise a variety of different materials. As statedpreviously, the material may comprise liquids such as blood, water, oilor chemicals. The various types of carbon bondings such as C—H, C—O,C—P, C—S or C—N may be provided for detection. The system may alsodetect various types of bondings between carbon atoms such as a singlebond (methane or Isooctane), dual bond items (butadiene and benzene) ortriple bond carbon items such as acetylene.

The sample 1210 may include detectable items such as organic compoundsincluding carbohydrates, lipids (cylcerol and fatty acids), nucleicacids (C,H,O,N,P) (RNA and DNA) or various types of proteins such aspolyour of amino NH₂ and carboxyl COOH or aminos such as tryptophan,tyrosine and phenylalanine. Various chains within the samples 1210 mayalso be detected such as monomers, isomers and polymers. Enzymes such asATP and ADP within the samples may be detected. Substances produced orreleased by glands of the body may be in the sample and detected. Theseinclude items released by the exocrine glands via tube/ducts, endocrineglands released directly into blood samples or hormones. Various typesof glands that may have their secretions detected within a sample 1210include the hypothalamus, pineal and pituitary glands, the parathyroidand thyroid and thymus, the adrenal and pancreas glands of the torso andthe hormones released by the ovaries or testes of a male or female.

The sample 1210 may also be used for detecting various types ofbiochemical markers within the blood and urine of an individual such asmelanocytes and keratinocytes. The sample 1210 may include various partsof the body to detect defense substances therein. For example, withrespect to the skin, the sample 1210 may be used to detect carotenoids,vitamins, enzymes, b-carotene and lycopene. With respect to the eyepigment, the melanin/eumelanin, dihydroxyindole or carboxylic may bedetected. The system may also detect various types of materials withinthe body's biosynthetic pathways within the sample 1210 includinghemoglobin, myoglobin, cytochromes, and porphyrin molecules such asprotoporphyrin, coporphyrin, uroporphyrin and nematoporphyrin. Thesample 1210 may also contain various bacterial to be detected such aspropion bacterium, acnes. Also various types of dental plaque bacteriamay be detected such as porphyromonos gingivitis, prevotella intremediand prevotella nigrescens. The sample 1210 may also be used for thedetection of glucose in insulin within a blood sample 1210. The sample1210 may also include amyloid-beta detection. Detection of amyloid-betawithin the sample may then be used for determinations of early onsetAlzheimer's. Higher levels of amyloid-beta may provide an indication ofthe early stages of Alzheimer's. The sample 1210 may comprise anymaterial that is desired to be detected that provides a unique OAM twistto a signal passing through the sample.

The orbital angular momentum within the beams provided within the sample1210 may be transferred from light to matter molecules depending uponthe rotation of the matter molecules. When a circularly polarized laserbeam with a helical wave front traps a molecule in an angular ring oflight around the beam axis, one can observe the transfer of both orbitaland spin angular momentum. The trapping is a form of optical tweezingaccomplished without mechanical constraints by the ring's intensitygradient. The orbital angular momentum transferred to the molecule makesit orbit around the beam axis as illustrated at 2402 of FIG. 24. Thespin angular momentum sets the molecule spinning on its own axis asillustrated at 2404.

The output OAM wave 1212 from the sample 1210 will have an orbitalangular momentum associated therewith that is different from the orbitalangular momentum provided on the input OAM wave 1208. The difference inthe output OAM wave 1212 will depend upon the material contained withinthe sample 1210 and the concentration of these materials within thesample 1210. Differing materials of differing concentration will haveunique orbital angular momentums associated therewith. Thus, byanalyzing the particular orbital angular momentum signature associatedwith the output OAM wave 1212, determinations may be made as to thematerials present within the sample 1210 and the concentration of thesematerials within the sample may also be determined.

Referring now to FIG. 25, the matching module 1214 receives the outputorbital angular momentum wave 1212 from the sample 1210 that has aparticular signature associated therewith based upon the orbital angularmomentum imparted to the waves passing through the sample 1210. Thematching module 1214 amplifies the particular orbital angular momentumof interest in order to provide an amplified wave having the desiredorbital angular momentum of interest 1216 amplified. The matching module1214 may comprise a matching aperture that amplifies the detectionorbital angular momentum associated with a specific material orcharacteristic that is under study. The matching module 1214 may in oneembodiment comprise a holographic filter such as that described withrespect to FIGS. 15A-15D in order to amplify the desired orbital angularmomentum wave of interest. The matching module 1214 is established basedupon a specific material of interest that is trying to be detected bythe system. The matching module 1214 may comprise a fixed module usingholograms as illustrated in FIGS. 15A-15D or a tunable module in amanner similar to that discussed with respect to the OAM generationmodule 1206. In this case, a number of different orbital angularmomentums could be amplified by the matching module in order to detectdiffering materials or differing concentrations of materials within thesample 1210. Other examples of components for the matching module 1214include the use of quantum dots, nanomaterials or metamaterials in orderto amplify any desired orbital angular momentum values within a receivedwave form from the sample 1210.

Referring now to FIG. 26, the matching module 1214 rather than usingholographic images in order to amplify the desired orbital angularmomentum signals may use non-linear crystals in order to generate higherorbital angular momentum light beams. Using a non-linear crystal 2602, afirst harmonic orbital angular momentum beam 2604 may be applied to anon-linear crystal 2602. The non-linear crystal 2602 will create asecond order harmonic signal 2606.

Referring now to FIG. 27, there is more particularly illustrated thedetector 1218 to which the amplified orbital angular momentum wave 1216from the matching circuit 1214 in order that the detector 1218 mayextract desired OAM measurements 2602. The detector 1218 receives theamplified OAM waves 1216 and detects and measures observable changeswithin the orbital angular momentum of the emitted waves due to thepresence of a particular material and the concentration of a particularmaterial under study within the sample 1210. The detector 1218 is ableto measure observable changes within the emitted amplified OAM wave 1216from the state of the input OAM wave 1208 applied to the sample 1210.The extracted OAM measurements 2702 are applied to the user interface1220. The detector 618 includes an orbital angular momentum detector2104 for determining a profile of orbital angular momentum states of theorbital angular momentum within the orbital angular momentum signal 616and a processor 2106 for determining the material within the sampleresponsive to the detected profile of the orbital angular momentumstates of the orbital angular momentum. The manner in which the detector1218 may detect differences within the orbital angular momentum is moreparticularly illustrates with respect to FIG. 28-30.

FIG. 28 illustrates the difference in impact between spin angularpolarization and orbital angular polarization due to passing of a beamof light through a sample 2802. In sample 2802 a, there is illustratedthe manner in which spin angular polarization is altered responsive to abeam passing through the sample 2802 a. The polarization of a wavehaving a particular spin angular momentum 2804 passing through thesample 2802 a will rotate from a position 2804 to a new position 2806.The rotation occurs within the same plane of polarization. In a similarmanner, as illustrated with respect to sample 2802 b, an image appearsas illustrated generally at 2808 before it passes through the sample2802 b. Upon passing the image through the sample 2802 b the image willrotate from the position illustrated at 2810 to a rotated positionillustrated at 2812. The amount of rotation is dependent upon thepresence of the material being detected and the level of concentrationof the material being detected within the sample 2802. Thus, as can beseen with respect to the sample 2802 of FIG. 28, both the spin angularpolarization and the orbital angular momentum will change based upon thepresence and concentration of materials within the sample 2802. Bymeasuring the amount of rotation of the image caused by the change inorbital angular momentum, the presence and concentration of a particularmaterial may be determined.

This overall process can be more particularly illustrated in FIG. 29. Alight source 2902 shines a light beam through expanding optics 2904. Theexpanded light beam is applied through a metalab generated hologram 2906that imparts an orbital angular momentum to the beam. The twisted beamfrom the hologram 2906 is shined through a sample 2908 having aparticular length L. As mentioned previously, the sample 2908 may belocated in a container or in its naturally occurring state. This causesthe generation of a twisted beam on the output side of the sample 2908to create a number of detectable waves having various orbital angularmomentums 2910 associated therewith. The image 2912 associated with thelight beam that is applied to sample 2908 will rotate an angle φdepending upon the presence and concentration of the material within thesample 2908. The rotation φ of the image 2912 is different for eachvalue orbital angular momentum −1 or +1. The change in rotation of theimage Δφ may be described according to the equation:Δφ=φ₁−φ⁻¹ =f(1,L,C)Where 1 is orbital angular momentum number, L is the path length of thesample and C is the concentration of the material being detected.

Thus, since the length of the sample L is known and the orbital angularmomentum may be determined using the process described herein, these twopieces of information may be able to calculate a concentration of thematerial within the provided sample.

The above equation may be utilized within the user interface moreparticularly illustrated in FIG. 30. The user interface 1220 processesthe OAM measurements 3002 using an internal algorithm 3002 that providesfor the generation of material and/or concentration information 3004that may be displayed in some type of user display. The algorithm wouldin one embodiment utilize that equation described herein above in orderto determine the material and/or concentration based upon the length ofa sample and the detected variation in orbital angular momentum. Theprocess for calculating the material and/or concentration may be done ina laboratory setting where the information is transmitted wirelessly tothe lab or the user interface can be associated with a wearable deviceconnected to a meter or cell phone running an application on the cellphone connected via a local area network or wide area network to apersonal or public cloud. The user interface 3020 of the device caneither have a wired or wireless connection utilizing Bluetooth, ZigBeeor other wireless protocols.

Referring now to FIG. 31, there is illustrated the manner in which thevarious data accumulated within the user interface 1220 that has beencollected in the manner described herein above may be stored andutilized for higher level analysis. Various devices 3102 for collectingdata as described herein above may communicate via private networkclouds 3104 or with a public cloud 3106. When communicating with aprivate cloud 3104, the devices 3102 merely store information that isassociated with a particular user device that is for use with respect toanalysis of the user associated with that user device. Thus, anindividual user could be monitoring and storing information with respectto their present glucose concentrations in order to monitor and maintaintheir diabetes.

Alternatively, when information is compiled from multiple devices 3102within the public cloud 3106, this information may be provided directlyto the public cloud 3106 from the individual devices 3102 or through theprivate clouds 3104 of the associated network devices 3102. Utilizingthis information within the public cloud 3106 large databases may beestablished within servers 3108 associated with the public cloud 3106 toenable large scale analysis of various health related issues associatedwith the information processed from each of the individual devices 3102.This information may be used for analyzing public health issues.

Thus, the user interface 1220 in addition to including the algorithm3002 for determining material and/or concentration information 3004 willinclude a wireless interface 3006 enabling the collected information tobe wirelessly transmitted over the public or private cloud as describedwith respect to FIG. 31. Alternatively, the user interface may comprisea storage database 3008 enabling the collected information to be locallystored rather than transmitted wirelessly to a remote location.

Referring now to FIG. 32, there is illustrated a particular example of ablock diagram of a particular apparatus for measuring the presence anconcentration of glucose using the orbital angular momentum of photonsof a light beam shined through a glucose sample. While the presentexample is with respect to the detection of glucose, one skilled in theart would realize that the example would be applicable to the detectionof the presence and concentration of any material. The process creates asecond-order harmonic with helical light beam using a non-linear crystalsuch as that described with respect to FIG. 25. The emission module 2402generates plane electromagnetic waves that are provided to an OAMgeneration module 3204. The OAM generation module 3204 generates lightwaves having an orbital angular momentum applied thereto using hologramsto create a wave having an electromagnetic vortex. The OAM twisted wavesare applied to the sample 3206 that is under study in order to detectthe glucose and glucose concentration within a sample. A rotatedsignature exits the sample 3206 in the manner described previously withrespect to FIGS. 28-29 and is provided to the matching module 3208. Thematching module 3208 will amplify the orbital angular momentum such thatthe observed concentrations may be calculated from the orbital momentumof the signature of the glucose. These amplified signals are provided todetection module 3210 which measures the radius of the beam w(z) or therotation of the image provided to the sample via the light beam. Thisdetected information is provided to the user interface that includes asensor interface wired or wireless Bluetooth or ZigBee connection toenable the provision of the material to a reading meter or a user phonefor the display of concentration information with respect to the sample.In this manner concentrations of various types of material as describeherein may be determined utilizing the orbital angular momentumsignatures of the samples under study and the detection of thesematerials or their concentrations within the sample determine asdescribed.

Provided the orthogonality of Laguerre polynomials, Laguerre Gaussianbeams exhibiting orbital angular momentum (OAM) have been determined asa basis for spatial division multiplexing (SDM) in communicationapplications using for example a mux-demux optical element design. OAMbeams are also of interest in quantum informatics. OAM also enables theprobing of solutions of chiral and non-chiral molecules.

FIG. 33 illustrates a further optical configuration for transmitting anddetecting information. The twisted nematic LCOS SLM 3302 implements a1024×768 array with 9 μm pitch and 8-bit resolution covering the visiblewavelength range (430-650 nm) and readily interfaced via a VGAconnection. A programmable SLM 3302 allows for the generation of avariety of engineered beams. A twisted nematic (TN) liquid crystal onsilicon (LCOS) SLM is particularly useful in realizing the hologramsthat modulate the phase front of the input plane wave 102 (FIG. 1) orGaussian beam. An SLM is computer addressable using common softwarepackages such as Matlab or Mathematica to define an arbitrarytwo-dimensional phase shift imprinted onto the beam input using, forexample, a hologram.

A collimated input beam is reflected off of a display appropriatelyencoded by a phase retarding forked gratings, or hologram. Thegenerating equation for the forked gratings may be written as a Fourierseries:

${T( {r,\varphi} )} = {\sum\limits_{m = {- \infty}}^{\infty}\;{t_{m}\mspace{14mu}{\exp\lbrack {- {{im}( {{\frac{2\pi}{D}r\mspace{14mu}\cos\mspace{14mu}\varphi} - {\ell\varphi}} )}} \rbrack}}}$

Where r and φ are the coordinates, l is the order of the vorticity and Dis the period of the rectilinear grating far from the forked pole. Theweights, t_(m), of the Fourier components of the phase grating may bewritten in terms of Bessel functions of integer order:t _(m)=(−i)^(m) J _(m)(kβ)exp(ikα).

Where kα and kβ bias and modulate the phase of the forked grating,respectively. Typically only a handful of terms of this series areneeded to generate the OAM beams. For example, success has been had withthe transfer pattern:

${T( {r,\varphi} )} = {\frac{1}{2} - {\frac{1}{2}\sin\mspace{14mu}( {{\frac{2\pi}{D}r\;\cos\;\varphi} - {\ell\varphi}} )}}$

Referring now back to FIG. 33, there is illustrated the opticalconfiguration for detecting a unique signature of a signal passingthrough a sample under test 3303. The sample 3303 may be in a containeror in its naturally occurring state. At a high-level, the instrumentcomprises a Mach Zehnder interferometer. One arm of the interferometerpropagates a reference beam 3310. The reference beam 3310 is created bya laser 3304 generating a light beam including a plurality of planewaves that is transmitted through a telescope 3306. The plane wave lightbeam from the telescope 3306 passes through a first beam splitter 3308.The beam splitter 3308 generates the reference beam 3310 that isreflected from a mirror 3311 to an interfering circuit 3312. Thereference beam 3310 may be a plane wave or, with the addition of a lens,a spherical wavefront may be implemented. This arm is blocked foramplitude only measurements.

In a second arm, the split plane wave beam from the beam splitter 3308is combined at a beam combiner 3314 with the beam provided from thespatial light modulator 3302. The spatial light modulator 3302 providesa light beam including the forked hologram 3316. The beam combiner 3314combines the forked hologram beam 3318 from the SLM 3302 and a planewave beam 3320 from the laser 3304 to generate an OAM or otherorthogonal function twisted beam of a known signature. This beam isreflected through a series of mirrors 3322 and focused on a pinholeaperture 3324 before passing the beam having the known orbital angularmomentum through the sample under test 3303.

The sample twisted beam 3326 has been interfered at the signal combiner3312 with the reference beam 3310. This interfered image may then berecorded by a camera or recording device 3328. This provides a uniqueOAM signature 3330 that may be analyzed in order to detect materialswithin the sample under test 3303. As can be seen, the unique OAMsignature 3330 is different from the signature 3332 of the transmittedbeam. The manner in which the signature is altered will be more fullydescribed herein below.

In the second arm, the LCOS SLM 3302 is used to transform a collimatedplane wave input beam 3320 into an OAM encoded beam. The SLM 3302 isdriven by a Matlab programs on an extended laptop display to provide adisplay of a forked hologram of any l or ρ. Following the SLM 3302, thebeam is reflected through three mirrors 3322 to provide a sufficientdistance for the separation of the diffracted OAM modes such that apinhole iris aperture 3324 may select the desired mode to pass through asample under test 3303.

Several materials of interest may be detected with OAM signatures usingthe setup of FIG. 33. Examples of these materials include acetone,isopropyl alcohol, sucrose, amyloid-beta, and glucose in steam distilledwater. Spectroscopic grade soda lime glass cuvettes (1 cm×2.5 cm×3 cm)or larger custom-made circular cuvettes having BK7 cover glass in capsmay be utilized for containing the sample under test 3303.

The sample under test 3303 is mounted on a translation stage arranged toallow quick and repeatable positioning in and out of the beam patheither by movement of the sample or movement of the beam projectionapparatus. Additionally, back reflections from the sample services aremonitored carefully and blocked by irises so no spurious, secondaryinteractions occur. The optical power through samples is low (less than25 μW) to avoid any refractive index dependent thermal gradients in thesolution.

The insertion of wave plates, variable retarders and polarizers beforeand after the sample under test has not revealed any remarkable results.While glucose is well-known to have a polarimetric response at thesewavelengths, the concentration path length product is too small toproduce a notable shift in the state of polarization. This suggests thatthe OAM and glucose is a more pronounced response then polarimetry ofthe molecule.

Images 3330 of the beam at the output of the instrument are recordedusing the high-resolution DSLR camera 3328 that is securely mountedperpendicular to the beam propagation direction and remotely triggeredto prevent vibration or shift in the instrument. Measurement ofellipticity is performed using Photoshop and Matlab or similar types ofimage measuring and processing software or applications.

With this instrument, the change to an OAM state imparted on the inputbeam by a sample under test 3303 can be quantified in both intensity andphase. A series of experiments has been performed using primarilyaqueous glucose solutions. A 15% stock solution was diluted to a varietyof desired concentrations. Because the different isomers of the sugarinteract with each other before attaining equilibrium, a settling timeis required for a new or altered solution. Solutions were allowed toequilibrate overnight (approximately 15 hours), a time much longer thanthe recommended 2 hours, in a Cuvette that was capped to preventevaporation.

As mentioned previously with respect to FIG. 1, passing through thesample 3303 causes a unique OAM signature to be imparted to the lightbeam passing through the sample. This unique OAM signature provides anidentification of the presence of a material within the sample and ofthe concentration of the material within the sample. This unique OAMsignature includes a number of differences from the OAM signal signaturethat is input to the sample 3303. The unique OAM signaturecharacteristics are illustrated in FIGS. 34-36. FIG. 34 illustrates themanner in which the ellipticity of the OAM intensity diagram changesafter passing through the sample 3303. Initially, as illustrated at3402, the intensity diagram has a substantially circular shape from theplane wave OAM beam before passing through the sample 3303. Afterpassing through the sample 3303, the intensity diagram has a much moreelliptical shape as illustrated generally at 3404. This elliptical shapeis a unique characteristic that is different depending upon a materialbeing detected and the concentration of the substance being detected. Bydetecting the ellipticity of the intensity diagram, a determination maybe made of the presence of a particular material within the sample.

FIG. 35 illustrates a further characteristic of the OAM signature thatmay be altered by passing through a sample 3303. In this case, thecenter of gravity of the intensity diagram has been shifted. Position3502 illustrates the initial position of the center of gravity of theintensity diagram before passing through a sample 3303. After passingthrough the sample 3303, the center of gravity moves to location 3504that is a noticeable shift from the original position prior to passingthrough the sample. The shift is uniquely affected by differentmaterials. Thus, the shift in center of gravity may also be used as anOAM distinct signature characteristic with the center of gravity shiftindicating the presence of a particular material and the concentrationof the material. Based upon an analysis of the shift in the center ofgravity of the intensity diagram, a determination of the presence and/orconcentration of a material may be made.

A final distinct OAM signature characteristic is illustrated in FIG. 36.In this case, the major axis 3602 of the intensity diagram ellipseshifts from a first position 3602 to a second position 3604 over anangle θ 3606. The major axis of the intensity diagram ellipse rotatesfrom a position 3602 to position 3604 based upon the material beingdetected. The angle θ is uniquely associated with a particular substanceand concentration of the substance being detected. Thus, a material maybe detected based upon a determined angle θ within the intensitydiagram.

A mathematical model may be used to represent the unique OAM signaturesprovided by each of changes in eccentricity, shift or translation of thecenter of gravity in rotation of the axis. The change in eccentricitymay be represented by:

$ {circle}\Rightarrow{x^{2} + y^{2} + z^{2}}\Rightarrow{\lbrack {x\mspace{14mu} y\mspace{14mu} z} \rbrack\begin{bmatrix}x \\y \\z\end{bmatrix}} $$ {3\text{-}{dimensional}\mspace{14mu}{ellipse}}\Rightarrow{{\lbrack {x\mspace{14mu} y\mspace{14mu} z} \rbrack\begin{bmatrix}{1\text{/}a^{2}} & 0 & 0 \\0 & {1\text{/}b^{2}} & 0 \\0 & 0 & {1\text{/}c^{2}}\end{bmatrix}}\begin{bmatrix}x \\y \\z\end{bmatrix}} $Where a, b, c are dimensions of the ellipse.

The change in the center of gravity may be represented by a shift ortranslation in space of a vector v according to the matrix:

$ {translation}\Rightarrow\begin{bmatrix}1 & 0 & v_{x} \\0 & 1 & v_{y} \\0 & 0 & v_{z}\end{bmatrix} $

The rotations of the axis may be represented by a series of matricesshowing rotations in 3-different orientations:

${\begin{bmatrix}1 & 0 & 0 \\0 & {\cos\mspace{14mu}\alpha} & {{- \sin}\mspace{14mu}\alpha} \\0 & {\sin\mspace{14mu}\alpha} & {\cos\mspace{14mu}\alpha}\end{bmatrix}\begin{bmatrix}{\cos\mspace{14mu}\beta} & 0 & {\sin\mspace{14mu}\beta} \\0 & 1 & 0 \\{{- \sin}\mspace{14mu}\beta} & 0 & {\cos\mspace{14mu}\beta}\end{bmatrix}}\begin{bmatrix}{\cos\mspace{14mu}\gamma} & {{- \sin}\mspace{14mu}\gamma} & 0 \\{\sin\mspace{14mu}\gamma} & {\cos\mspace{14mu}\gamma} & 0 \\0 & 0 & 1\end{bmatrix}$

Rotation by α Rotation by β Rotation by γ

In an example illustrated in FIGS. 37A and 37B there is shown theapplication of an OAM beam to a sample consisting only of water (FIG.37A) and of water including a 15% glucose concentration (FIG. 37B). Anl=7 OAM beam at 543 nm is propagated through a 3 cm Cuvette of onlywater to provide the intensity diagram illustrated in FIG. 37A. Theintensity diagram illustrated in FIG. 37B is provided when the l=7 OAMbeam passes through a 15% glucose solution in water. The OAM signaturemanifests itself as an induced ellipticity on the ordinary circular beamamplitude illustrated in the intensity diagram of FIG. 37A. The distinctsignature effect may also be observed in phase diagrams such as thatillustrated in FIGS. 38A and 38B. FIGS. 38A and 38B illustrateinterferograms of an l=2 OAM beam at 633 nm propagating through a 3 cmcuvette of water (FIG. 38A) and a 3 cm cuvette of 15% glucose in water(FIG. 38B). In this particular interferance, the reference beams havethe same spherical wave fronts. This is why essentially spiral patternis observed in the phase measurements. Note in particular, the torsionalshift in one of the 2 spirals of the phase front of the samplepropagating through the glucose solution. The shift in the spiralpattern is the signature of the interaction in this experiment.

An unperturbed OAM mode propagates through several meters of free space.Glucose samples appear to impart a phase perturbation on an OAM beamcausing the OAM mode to topologically be involved in the propagationdirection. This effect allows for more sensitive metrology. FIG. 39shows the amplitude of an OAM beam and FIG. 40 shows the phase of an OAMbeam. The beam is an OAM l=beam and is perturbed when passing through a3 cm Cuvette of a 5% glucose solution and a plane four meters beyond theCuvette. The ellipticity of the beam is much more pronounced in bothamplitude and phase measurements.

The OAM signature is nonlinear with respect to glucose concentrationsand under some conditions, appears to be somewhat periodic withconcentration. The ellipticity as a function of glucose concentration isplotted in FIG. 41 using a 3 cm Cuvette, OAM modes l=5, 6, 7, forconcentrations of glucose between 5% and 9% in water. Though thepreliminary data is noisy, the trend persists over several OAM modes.

There is a broad absorption band for glucose centered at approximately750 nm, with a FWHM (Full Width Half Maximum), as understood by a personof skill in the art, of approximately 250 nm. Given that the 543 nmabsorbance of glucose is 4 times smaller than that for 633 nm, it isinteresting that the formal wavelength provides a stronger OAM response.This suggests the interaction is based on the real part of thesusceptibility, χ′, rather than its imaginary part, χ″. We note as wellthat in a separate polarimetry characterization of glucose, using samplecells as long as 20 cm, we measured a 50% larger specific rotation at543 nm than at 633 nm. In the OAM work, however, we found no discernablechange in the effect with polarization, nor did we observe a change inthe state of polarization of the beam through the 3 cm samples. This isin keeping with the previous polarization studies of OAM with chiralmolecules.

As a check for whether the vorticity of the OAM beam was important forthe effect, and annulus was used to project a simple ring of lightthrough a glucose sample. The annulus pattern was printed on atraditional plastic transparency sheet and illuminated with a magnifiedand collimated 543 nm laser beam. As can be seen in FIGS. 42A-42C, nodistortion or signature was observed through Cuvette's of water (FIG.42B) or Glucose (FIG. 42C) solution. Varying the ring diameter did notchange these no results, even for diameters larger than the typical OAMbeam. When the annulus diameter was larger than the Cuvette, obviousclipping was observed. The power level of the beams in this test was asmuch in order of magnitude higher than in the OAM experiments. Thus, anythermal effects would have been accentuated.

Since aqueous solutions of glucose were used in the experiments, thestudy of propagation of OAM in water is relevant. Steam distilled water,the solvent used in dilution, was placed in clean new cells of thevariety of links and cross-sections and propagation of a variety of OAMbeams through this medium was measured. No discernible differences wereobserved among an OAM mode propagated through a dry cell, a sample ofpath length 0.5 cm and a sample of 8 cm of water.

Another null result was observed in an experiment were in an OAM beamwas propagated through a liquid crystal that variable retarder. In FIG.43, reference Nos. 4302, 4304 and 4306 show an €=7 OAM mode at theoutput of a variable wave plate for differing drive voltages between 0.1V and 6 V.

It is been noted that the eccentricities of the intensity imagesproduced by shining orthogonal function processed beam through a samplecan have variances due to a number of differing factors. FIG. 44illustrates an example wherein a light beam produced by a laser 4402 isaltered by a hologram provided by an SLM 4404 to generate an OAM twistedbeam 4406. The OAM twisted beam in addition to being altered by OAMfunctions may also be processed using Hermite Gaussian functions,Laguerre Gaussian functions or any other type of orthogonal function.The OAM twisted beam is focused through a system 4408 of lenses andmirrors to direct the beam through a mode sorter 4410. The beam isseparated into its different modes when regenerated at mode sorter 4412and the intensity images may be registered by a camera 4414.

The beam from the laser 4402 has an inherent eccentricity ofapproximately 0.15. As illustrated in FIG. 45, there are illustratedvarious OAM modes produced by the SLM in column 4502 for l=5,4,3,2,1. Ascan be seen, there are differences between the eccentricity of the modesproduced by the SLM, and the eccentricity of the modes regenerated bythe second mode sorter 4412.

Measurements of eccentricity are performed using Photoshop and Matlab toidentify the specific signatures. Referring now to FIG. 46, there isillustrated an example of an ellipse 4602 having a radius “a” along itslong axis, a radius “b” along a short axis and a distance “c” to thefoci 4604 of the ellipse. The eccentricity of the ellipse is representedby the equation eccentricity=c/a. The eccentricity varies from 0 to 1with 0 representing a circle and 1 representing a line. The eccentricityequation is calculated according to the following equations:

$U_{xx} = {{\frac{1}{N}{\sum\limits_{i = 1}^{N}\; x_{i}^{2}}} + \frac{1}{12}}$$U_{yy} = {{\frac{1}{N}{\sum\limits_{i = 1}^{N}\; y_{i}^{2}}} + \frac{1}{12}}$$U_{xy} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}\;{y_{i}x_{i}}}}$${common} = \sqrt{( {U_{xx} - U_{yy}} )^{2} + {4U_{xy}^{2}}}$${2a} = {2\sqrt{2}\sqrt{{U_{xx}U_{yy}} + {common}}}$${2b} = {2\sqrt{2}\sqrt{{U_{xx}U_{yy}} - {common}}}$$c = \sqrt{a^{2} - b^{2}}$ ${Eccentricity} = \frac{c}{a}$where x_(i) is the x location of the pixels in the ellipse; y_(u) is they locations of the pixels in the ellipse; and N is the number of pixelsin the ellipse.

It is been found that the eccentricity is greater than 0 when no sampleis present within the cuvette. A number of factors contribute to thenonzero eccentricity. OAM twisted signals have been found to providedifferent eccentricities based upon a number of different factors thatmay affect the index of refraction. These factors include things such asthe sample distribution of the material within the cuvette due togravity, the distance of the camera from the spatial light modulator andthe camera angle of the camera from the spatial light modulator. Otherfactors affecting the eccentricity are the cuvette positioning, theindex of refraction changes do to the sample, the cuvette shape and thebeam incidence and exit angle from the cuvette.

Several image processing factors have also been determined not to causechanges that are outside the margin of error. Changes based on softwareprocessing errors, a circular mask that is not OAM, the sample sittingtime or the sample interaction with the glass or plastic comprising thesample container may provide eccentricity changes, but the changes arenot due to optical impairments caused by the cuvette orientation, cameraalignment, etc. These factors do produce some changes in eccentricity,but they are within the margin of error and the majority of theeccentricity change is based on the signature of the molecule beingdetected.

Referring now to FIG. 47, there is illustrated a flow diagram foranalyzing intensity images taken by the camera 4414. The intensity imagehas applied thereto threshold double precision amplitude to enable thering to be clearly seen without extra pixels outside of the ring at step4702. Next at step 4701, both columns and rows are scanned along for theentire image. The peaks of the two largest hills and their locations aredetermined at step 4706. An ellipse is fit at step 4008 for all peaklocations found. Finally, at step 4710, a determination is made of themajor and minor axis of the ellipse, the focal point of the ellipse, thecentroid, eccentricity and orientation of the ellipse.

FIG. 48 illustrates an ellipse fitting algorithm flowchart. The X and Ypixel locations are input at step 4802 for all peaks that are found. Aninitial guess is provided at step 4804 for the conic equationparameters. The conic equation parameters comprise parameters A, B, C, Dand E for the equation Ax²+By²+Cx+Dy+E=0. The conjugate gradientalgorithm is used at step 4806 to find conic equation parameters thatprovide an optimal fit. An orientation of the ellipse is determined atstep 4808 and moved to determine the major and minor axis. Thedetermination of step 4808 is determined according to the equation

$\varnothing = {\frac{1}{2}\tan^{- 1}\frac{B}{C - A}}$The ellipse orientation is returned at step 4810 to determine thecentral point of the ellipse. Finally, at step 4812, a determination ismade if the conic equation represents an ellipse. For an ellipseparameters A and B will exist and have the same sign but will not beequal. Based upon this analysis it is been determined that lateral shiftof up to 1 mm can cause significant changes in the measured eccentricitydue to clipping of up to 0.2.Fractional OAM Signals

Molecular spectroscopy using OAM twisted beams can leverage fractionalOAM states as a molecular signature along with other intensitysignatures (i.e. eccentricity, shift of center of mass and rotation ofthe elliptical intensity) as well as phase signatures (i.e. changes inthe phase of the scattered beam) and specific formation of publicitydistributed spectrum. The method of optical orientation of electronicsbeen by circularly polarized photons has been heavily used to study spinangular momentum in solid state materials. The process relies onspin-orbit coupling to transfer angular momentum from the spin ofprotons to the spin of electrons and has been Incorporated intopump-probe Kerr and Faraday rotation experiments to study the dynamicsof optically excited spends. By enabling the study is spin decoherence,transport and interactions, this strategy has played a role in thedevelopment of semiconductor spintronics.

The proposed spectroscopy technique focuses instead on localized orbitalangular momentum (OAM) and solids. Specifically, one can distinguishbetween delocalized OAM associated with the envelope wave function whichmay be macroscopic in spatial extent, and local OAM associated withatomic sites, which typically is incorporated into the effect of spinand associated electronic states. The former type of angular momentum isa fundamental interest to orbital fleet coherent systems, for example,quantum Hall layers, superconductors and topological insulators.Techniques to study non-equilibrium delocalized OAM in these and othersystems create opportunities to improve understanding of scattering andquantum coherence of chiral electronic states, with potentialimplications for materials discovery.

The interaction of light with glucose in beta amyloid and thespectroscopy applications of OAM with respect to these. Additionally thetransfer of OAM between acoustic and photonic modes in an ellipticalfiber, the generation of Rahman sideband carrying OAM, OAM using apleasant Monica lens, the study of optically coherent OAM in excite onsusing for wave mixing in the application of linearly polarized light tocreate a 2-D pleasant Monica analog to OAM light in patterned sinmetallic film, and the possibility of OAM light producing spin polarizedvote till electronics for efficient semiconductors may also findapplication in these techniques.

Referring now to FIG. 49, one manner for using nested fractional OAMstates to alleviate the problems associated with integer OAM states andto enable the use of stable states of fractional OAM for similarpurposes as those described herein above. In this case the input signals4902 are provided to fractional OAM generation circuitry 4904. Thefractional OAM generation circuitry 4904 generates output signals 4906having fractional orthogonal states which may then be further applied ordetected as discussed herein.

The orbital angular momentum of light beams is a consequence of theirazimuthal phase structure. Light beams have a phase factor exp(imφ),where m is an integer and φ is the azimuthal angle, and carry orbitalangular momentum (OAM) of mℏ per photon along the beam axis. These lightbeams can be generated in the laboratory by optical devices, such asspiral phase plates or holograms, which manipulate the phase of thebeam. In cases where such a device generates an light beam with aninteger value of m, the resulting phase structure has the form of |m|intertwined helices of equal phase. For integer values of m, the chosenheight of the phase step generated by the optical device is equal to themean value of the OAM in the resulting beam.

Recently, spiral phase steps with fractional step height as well asspatial holograms have been used to generate light beams with fractionalOAM states. In these implementations, the generating optical deviceimposes a phase change of exp(iMφ) where M is not restricted to integervalues. The phase structure of such beams shows a far more complexpattern. A series of optical vortices with alternating charge is createdin a dark line across the direction of the phase discontinuity imprintedby the optical device. In order to obtain the mean value of the orbitalangular momentum of these beams, one has to average over the vortexpattern. This mean value coincides with the phase step only for theinteger and half integer values. There are certainly more connectionsbetween optics and quantum theory to represent beams with fractional OAMas quantum states.

The theoretical description of light modes with fractional OAM is basedon the generating optical device. For integer OAM values, a theoreticaldescription may exist which provides the way to treat the angle itselfas quantum mechanical Hermitian operator. The description can providethe underlying theory for a secure quantum communication system and giveform to the uncertainty relation for angle and angular momentum. Thetheory may be generalized for fractional values of M thereby creating aquantum mechanical description of fractional OAM. Such a rigorousformulation is of particular interest is the use of half integer spiralphase plates have been used to study high dimensional entanglement.Fractional OAM states are characterized not only by the height of thephase step, but also by the orientation of the phase dislocation α. Forhalf odd integer values of M, M mod 1=½, states with the same M but a πdifference in a are orthogonal. In light of recent applications ofinteger OAM in quantum key distribution in the conversion of spin toorbital angular momentum in an optical medium, a rigorous formulation isimportant for possible applications of fractional OAM to quantumcommunication.

The component of the OAM in the propagation direction Lz and theazimuthal rotation angle form a pair of conjugate variables (just liketime-frequency or space-momentum). Unlike linear position and momentum,which are both defined on an unbound and continuous state space, thestate spaces for OAM and the rotation angle are different in nature. TheOAM eigenstates form a discrete set of states with m taking on allinteger values. Eigenstates of the angle operator are restricted to a 2πradian interval since it is physically impossible to distinguish betweenrotation angles differing by less than 2π radians. The properties of theangle operator are rigorously derived in an arbitrarily large, yetfinite state space of 2L+1 dimensions. This space is spanned by theangular momentum states |m

with m ranging from −L, −L+1, . . . , L. Accordingly, the 2π radianinterval [θ0, θ0+2η) is spanned by 2L+1 orthogonal angle states |θn

with θn=θ0+2πn/(2L+1). Here, θ₀ determines the starting point of theinterval and with it a particular angle operator φ^θ. Only afterphysical results have been calculated within this state space is Lallowed to tend to infinity, which recovers the result of an infinitebut countable number of basis states for the OAM and a dense set ofangle states within a 2π radian interval.

A quantum state with fractional OAM is denoted by |M

, where M=m+μ and m is the integer part and μ∈[0, 1) is the fractionalpart. The state |M

is decomposed in angle states according to:

$ {  { | M  \rangle =  {( {{2L} + 1} )^{- \frac{1}{2}}{\sum\limits_{n = 0}^{2L}\;{\exp( {{iM}\;\theta_{n}} )}}} \middle| \theta_{n} } \rangle \middle| M \rangle =  {( {{2L} + 1} )^{- \frac{1}{2}}{\sum\limits_{n = 0}^{2L}\;{{\exp( {{im}\;\theta_{n}} )}\mspace{14mu}{\exp( {i\;{\mu\theta}_{n}} )}}}} \middle| \theta_{n} } \rangle$It is important to note that α is bounded by 0≤α<2π, so that theorientation of the discontinuity is always understood as measured fromθ₀. With this construction the fractional state |M

can be written as:

$ { | {M(\alpha)}  \rangle =  {( {{2L} + 1} )^{- \frac{1}{2}}{\exp( {i\;{\mu\alpha}} )}{\sum\limits_{n = 0}^{2L}\;{{\exp( {{iM}\;\theta_{n}} )}\mspace{14mu}{\exp\lbrack {i\; 2{\pi\mu}\;{f_{\alpha}( \theta_{n} )}} \rbrack}}}} \middle| \theta_{n} } \rangle$

In integer based OAM generation applications light beams may begenerated using a spiral phase plate. However, light beams generatedusing a spiral phase plate with a non-integer phase step are unstable onpropagation. However, one can generate light carrying fractional orbitalangular momentum beams not with a phase step of a spiral phase plate butby a synthesis of Laguerre-Gaussian modes. This may be accomplished asillustrated in FIG. 50 using a spatial light modulator 5002. Inputsignals 5004 are provided to the spatial light modulator 5002 and usedfor the generation of fractional OAM beams 5006. The spatial lightmodulator 5002 synthesizes Laguerre Gaussian modes rather than using aphase step of a spiral phase plate. By limiting the number of Gouyphases in the superposition, one can produce a light beam from the SLM5002 which is well characterized in terms of its propagation. Thestructural stability of these fractional OAM light beams from an SLMmake them ideal for communications using fractional OAM states.Additionally as will be described herein below the beams would be usefulfor concentration measurements of various organic materials.

Using the spatial light modulator 5002, a light beam with fractional OAMmay be produced as a generic superposition of light modes with differentvalues of m. As illustrated in FIG. 51, various Laguerre-Gaussian beammodes 5102 may have a superposition process 5104 applied thereto by thespatial light modulator 5002 in order to generate the fractional beamoutputs 5106. Using the correspondence between optics and quantumtheory, OAM can be represented as a quantum state. This quantum state5202 can be decomposed into a basis of integer OAM states 5204 asgenerally illustrated in FIG. 52. The decomposition only determines theOAM index m which in a superposition of LG beams leaves the index forthe number of concentric rings unspecified. Therefore, one can make useof this flexibility to find a representation of a fractional OAM statein terms of superimposed LG beams with a minimal number of Gouy phasesto increase propagation stability. One can produce these beams using thespatial light modulator 5002 and study their propagation and vortexstructure. Light beams constructed in this manner are in excellentrealization of non-integer OAM states and are more stable on propagationand light emerging from fractional faced steps of a spiral phase plate.

Referring now to FIG. 53, there is illustrated the manner in which anSLM may be programmed to provide fractional OAM beams. Rather than usingmultiple optical elements to generate each Laguerre Gaussian modeseparately a single SLM 5302 may be programmed with a hologram 5304 thatsets the phase structure 5306 and intensity structure 5308 forgenerating the superposition. A blazed grating 5310 is also included inthe hologram 5304 to separate angularly the first fractional order. Theformula for the resulting phase distribution of the hologram 5304 andrectilinear coordinates Φ(x,y)_(holo) is given by:

Φ(x, y)_(holo) = [Φ(x, y)_(beam) + Φ(x, Λ)_(grating)  mod  2π − π]sin  c²[(1 − I(x, y)_(beam))π] + π

In this equation Φ(x,y) beam is the phase profile of the superpositionat the beam waist for z=0 and Φ(x,Λ) grating is the phase profile of theblazed grating which depends on the period of the grating Λ. The twophase distributions are added to modulo 2π and, after subtraction of πare multiplied by an intensity mask. In regions of low intensity theintensity mask reduces the effect of the blazed grating 5310, which inturn leads to reduced intensity in the first diffraction order. Themapping between the phase depth and the desired intensity is not linearbut rather given by the trigonometric sinc function.

Referring now to FIG. 54 and FIG. 55, there are illustrated the stepsnecessary to generate a hologram for producing a non-integer OAM beam.Initially, at step 5502 a carrier phase representing a blazed grating5402 is added to the phase 5404 of the superposition modulo 2π. Thiscombined phase 5406 is multiplied at step 5504 by an intensity mask 5408which takes account of the correct mapping between the phase depth anddiffraction intensity 3010. The resulting hologram 5412 at step 5506 isa hologram containing the required phase and intensity profiles for thedesired non-integer OAM beam.

Referring now to FIG. 56, there are illustrated the intensity and phaseprofiles on propagation for a superposition of 10 modes and M=6.5.Intensity and phase profiles 5602, 5604 and 5606 show a sequence ofnumerical plots for three different propagation distances of z=0, z=2zRand z=4zR show the changes in the phase and intensity on propagationfrom the waist plane into the far field. The various cross-sections areplotted over a range of ±3w(z) for each value of z. Profiles 5608, 5610and 5612 show the corresponding experimental profiles.

The use of fractional OAM beams may be used in a number of fashions. Inone embodiment, as illustrated in FIG. 57, fractional OAM beams may begenerated from a fractional OAM beam generator 5702. These fractionalOAM beams are then shown through a sample 5704 in a manner similar tothat discussed herein above. OAM spectroscopy detection circuitry 5706may then be used to detect certain OAM fraction state profiles caused bythe OAM beam shining through the sample 5704. Particular OAM fractionstates will have a particular fractional OAM state characteristicscaused by the sample 5704. This process would work in the same manner asthat described herein above.

FIG. 58 illustrates one example of a OAM state profile that may be usedto identify a particular material within a sample. In this case, thehighest number of OAM states is illustrated at L=3. Additional statelevels are also illustrated at L=1.5; L=2.75; L=3.5 and L=4. Thisparticular OAM state profile would be uniquely associated with aparticular material and could be used to identify the material within asample when the profile was detected. The interaction of LaguerreGaussian light beams with glucose and beta amyloid have been the initialspectroscopy application of OAM to sample types.

The transfer of OAM between the acoustic and photonic modes in anoptical fiber, the generation of Raman side bands carrying OAM, OAMusing a plasmonic lens, the study of optically coherent OAM in excitonsusing four-wave mixing, the application of linearly polarized light tocreate a 2-D plasmonic analog to OAM light in a patterned thin metallicfilm and the possibility of OAM light producing spin polarizedphotoelectrons for efficient semiconductors are other potentialspectroscopy applications.

Other means of generation and detection of OAM state profiles may alsobe utilized. For example a pump-probe magneto-orbital approach may beused. In this embodiment Laguerre-Gaussian optical pump pulses impartorbital angular momentum to the electronic states of a material andsubsequent dynamics are studied with femto second time resolution. Theexcitation uses vortex modes that distribute angular momentum over amacroscopic area determined by the spot size, and the optical probestudies the chiral imbalance of vortex modes reflected off of a sample.There will be transients that evolve on timescales distinctly differentfrom population and spin relaxation but with large lifetimes.

Multi-Parameter Spectroscopy

A further application of the OAM spectroscopy may be further refined byidentifying items using a number of different types of spectroscopy toprovide a more definitive analysis. Referring now to FIG. 59, there isgenerally illustrated a multi-parameter spectroscopy system 5900. Aplurality of different spectroscopy parameters 5902 may be tracked andanalyzed individually. The group of parameters is then analyzed togetherusing multi-parameter spectroscopy analysis processor or system 5904 todetermine and identify a sample with output 5906. The differentspectroscopic techniques receive a light beam generated from a lightsource 5908, for example a laser, that has passed through a sample 5910that a material or concentration of material therein that is beingdetected. While the light source of FIG. 59 illustrates a single laserand light beam, multiple light sources may provide multiple light beamsor a single source may be used to provide multiple light beams. In oneexample, development of a single optical spectroscopy system to fullycharacterize the physical and electronic properties of small samples inreal time may be accomplished using the polarization, wavelength, andorbital angular momentum (OAM) of light. A polarized optical source isused to characterize the atomic and molecular structure of the sample.The wavelength of the source characterizes the atomic and molecularelectronic properties of the sample including their degree ofpolarizability. OAM properties of the source are principally used tocharacterize the molecular chirality, but such new techniques are notlimited to chiral molecules or samples and can be applied to non-chiralmolecules or samples. These three spectroscopy dimensions combine togreatly improve the process of identifying the composition of materials.Integrated into a compact handheld spectrometer, 3D or multi-parameterspectroscopy empowers consumers with numerous applications includinguseful real time chemical and biological information. Combined withother pump-probe spectroscopy techniques, 3D/muti-parameter spectroscopypromises new possibilities in ultrafast, highly-selective molecularspectroscopy. While the following description discusses a number ofdifferent spectroscopy techniques that may be implemented inmulti-parameter spectroscopy system 5900, it should be realized thatother spectroscopy techniques may be combined to provide themulti-spectroscopy analysis system of the present disclosure.

Optical Spectroscopy

Spectroscopy is the measurement of the interaction of light with variousmaterials. The light may either be absorbed or emitted by the material.By analyzing the amount of light absorbed or emitted, a materialscomposition and quantity may be determined.

Some of the light's energy is absorbed by the material. Light of a givenwavelength interacting with a material may be emitted at a differentwavelength. This occurs in phenomena like fluorescence, luminescence,and phosphorescence. The effect of light on a material depends on thewavelength and intensity of the light as well as its physicalinteraction with the molecules and atoms.

A schematic of a spectrometer which makes relative measurements in theoptical spectral region of the electromagnetic spectrum uses light thatis spectrally dispersed by a dispersing element is shown in FIG. 60. Inparticular, a device 6002, such as a monochromator, polychromator, orinterferometer, selects a specific wavelength from a light source 6004.This single-wavelength light interacts with a sample 6006. A detector6008 is used to measure the spectrum of light resulting from thisinteraction. A change in the absorbance or intensity of the resultinglight 6010 is measured as the detector 6008 sweeps across a range ofwavelengths. A range of different spectroscopic techniques, based onthese fundamental measurements, have been developed such as thosediscussed in A. Hind, “Agilent 101: An Introduction to OpticalSpectroscopy,” 2011.(http://www.agilent.com/labs/features/2011_101_spectroscopy.html) whichis incorporated herein by reference in its entirety. Here, attention isgiven to molecular spectroscopy techniques including infrared, Raman,terahertz, fluorescence, and orbital angular momentum spectroscopy.

Molecular Spectroscopy

Infrared Spectroscopy

Various types of molecular spectroscopy techniques may also be used inthe multi-parameter spectroscopy system. These techniques includeinfrared spectroscopy and others.

Infrared frequencies occur between the visible and microwave regions ofthe electromagnetic spectrum as shown in FIG. 61. The frequency, v,measured in Hertz (Hz), and wavelength, λ, 6102 typically measured incentimeters (cm) are inversely related according to the equations:

$v = {{\frac{c}{\lambda}\mspace{14mu}{and}\mspace{14mu}\lambda} = \frac{c}{v}}$where c is the speed of light (3×10¹⁰ cm/sec).

The energy of the light is related to A and v by

$E = {{hv} = \frac{hc}{\lambda}}$where h is Planck's constant (h=6.6×10⁻³⁴ J·s).

The infrared (IR) spectrum 6104 is divided into three regions: thenear-, mid-, and far-IR. The mid IR region includes wavelengths between3×10⁻⁴ and 3×10⁻³ cm.

In the process of infrared spectroscopy, IR radiation is absorbed byorganic molecules. Molecular vibrations occur when the infrared energymatches the energy of specific molecular vibration modes. At thesefrequencies, photons are absorbed by the material while photons at otherfrequencies are transmitted through the material.

The IR spectrum of different materials typically includes uniquetransmittance, T, peaks and absorbance troughs occurring at differentfrequencies such as the measured IR spectrum of water vapor shown inFIG. 62.

The absorbance, A, is related to the transmittance byA=log₁₀(1/T),Each material exhibits a unique infrared spectral fingerprint, orsignature, determined by its unique molecular vibration modes whichpermit identification of the material's composition by IR spectroscopy.In the case of water vapor (FIG. 62), for example, the water moleculesabsorb energy within two narrow infrared wavelengths bands that appearas absorbance troughs 6202.Molecular Vibrations

Referring now to FIG. 63, water molecules exhibit two types of molecularvibrations: stretching and bending. A molecule 6302 consisting of natoms 6308 has 3n degrees of freedom. In a nonlinear molecule likewater, three of these degrees are rotational, three are translational,and the remaining correspond to fundamental vibrations. In a linearmolecule 6302, two degrees are rotational and three are translational.The net number of fundamental vibrations for nonlinear and linearmolecules is therefore, 3n−6 and 3n−5, respectively.

For water vapor, there are two strong absorbance troughs 6202 (FIG. 62)occurring at approximately 2.7 μm and 6.3 μm as a result of the twostretching vibrational modes 6304 of water vapor and its bending mode6306, respectively. In particular, the symmetric and asymmetricstretching modes 6304 absorb at frequencies in very close proximity toeach other (2.734 μm and 2.662 μm, respectively) and appear as a single,broader absorbance band in FIG. 62 between the troughs 6202.

Carbon dioxide, CO₂, exhibits two scissoring and bending vibrations6402, 6404 (FIG. 64) that are equivalent and therefore, have the samedegenerate frequency. This degeneracy appears in the infrared spectrumof FIG. 65 at λ=15 μm. The symmetrical stretching vibrational mode 6404of CO₂ is inactive in the infrared because it doesn't perturb itsmolecular dipole moment. However, the asymmetrical stretching vibrationmode 6402 of CO₂ does perturb the molecule's dipole moment and causes anabsorbance in CO₂ at 4.3 μm as shown in FIG. 65.

Both molecular stretching and bending vibration modes of molecules(FIGS. 63 and 64) can be predicted to useful theoretical approximationusing simple classical mechanics models.

Stretching Vibrations

The stretching frequency of a molecular bond may be approximated byHooke's Law when treated as a simple classical harmonic oscillatorconsisting of two equal masses bound by a spring

$v = {\frac{1}{2\pi}\sqrt{\frac{k}{m}}}$where k is the force constant of the spring and m is the mass of anatom.

In the classical harmonic oscillator, the energy depends on the extentto which the spring is stretched or compressed,E=½kx ² =hvwhere x is the displacement of the spring. The classical model ofHooke's Law, however, is inconsistent with the absorbance of energy bymolecules as it would suggest that energy of any frequency is absorbed.In real molecules, vibrational motion is quantized and appropriatelymodeled by the quantum mechanical expression,E _(n)=(n+½)hvwhere n is the principal quantum number (n=0, 1, 2, 3 . . . )characteristic of each permitted energy level.

The lowest energy level is E₀=½hv followed by E₁=3/2hv. Only transitionsto the next energy level are allowed according to the selection rule.Subsequently, molecules absorb photonic energy in integer increments ofhv. For photon absorption energies of 2hv or 3 hv, however, theresulting absorbance bands are called overtones of the infrared spectrumand are of lesser intensity than fundamental vibrational bands.

Atomic bonds within molecules may come apart if stretched too far andcannot be compressed beyond a certain point. As such, molecules areactually anharmonic oscillators. The energy of an anharmonic oscillatoras a function of the interatomic distance is shown in FIG. 66 with anenergy minimum occurs at the normal bond length 6602 (equivalent to arelaxed classical mechanical spring). As the interatomic distanceincreases the quantized energy levels 6604 become more closely spacedand the energy reaches a maximum. The allowed transitions, hv becomesmaller in magnitude which gives lower overtone energies than wouldotherwise be predicted using the simply harmonic oscillator theorydepicted in FIG. 67.

Though this mathematical framework represents a useful, if not simple,approximation, the vibrational activity between two atoms in a largemolecule cannot be isolated from the vibrational behavior of other atomsin the molecule. Vibrations of two bonds within a molecule may becoupled in such a manner that one contracts or expands while the othercontracts as in either asymmetrical or symmetrical stretchingvibrations. When this occurs different absorbance frequency bands areobserved instead of superimposed, or degenerate, bands as observed whentwo identical atoms in a bond vibrate with an identical force constant.

Infrared spectroscopy is used to identify material species by theirunique vibrational and rotational optical signatures. A complementaryspectroscopy technique, Raman spectroscopy is used to identify materialsby their unique light-scattering signatures as discussed in the nextsection.

Raman Spectroscopy

Since Raman spectroscopy is a technique used to characterize a materialby the amount of light it scatters. Raman spectroscopy complementsinfrared spectroscopy which instead measures the amount of lightabsorbed by a material. Raman and infrared spectroscopy may further beused in conjunctions with OAM and polarization spectroscopy to furtherimprove analysis results. When light interacts with matter, changes inthe dipole moment of its molecules yield infrared absorption bands whilechanges in their polarizability produce Raman bands. The sequence ofobserved energy bands arises from specific molecular vibrations whichcollectively produce a unique spectral signature indicative of each typeof molecule. Certain vibrational modes occurring in Raman spectroscopyare forbidden in infrared spectroscopy while other vibrational modes maybe observed using both techniques or a multi-parameter technique usingOAM. When these latter modes are common to both techniques, theirintensities differ significantly.

The most frequent interaction of photons with molecules results inRayleigh scattering in which photons are elastically scattered as theresult of excited electrons that decay to their original energy level.Consequently, Rayleigh scattered photons have the same energy asincident photons.

With the discovery of inelastic photonic scattering phenomena in 1928 byC. V. Raman and K. S. Krishnan, Raman spectroscopy was established as apractical chemical analysis method useful to characterize a wide varietyof chemical species including solid, liquid, and gaseous samples. Solidcrystal lattice vibrations are typically active in Raman spectroscopyand their spectra appear in polymeric and semiconductor samples. Gaseoussamples exhibit rotational structures that may be characterized byvibrational transitions.

Approximately one percent of incident photons scatter inelastically, andyield lower energy photons. Raman scattering results from changes in thevibrational, rotational, or electronic energy of a molecule. Thevibrational energy of the scattering molecule is equivalent to thedifference between incident and Raman scattered photons. When anincident photon interacts with the electric dipole of a molecule, thisform of vibronic spectroscopy is often classically viewed as aperturbation of the molecule's electric field. Quantum mechanically,however, the scattering event is described as an excitation to a virtualenergy state lower in energy than a real electronic transition withnearly coincident decay and change in vibrational energy. Suchspectroscopy can work in conjunction with incident photons that carryOAM. In Raman spectroscopy, incident photons excite electrons to adifferent final energy level than its original energy level (FIG. 68).

Since the intensity of Raman scattering is low, heat produced by thedissipation of vibrational energy does not yield an appreciable rise inmaterial temperature. Such Raman spectroscopy can work in conjunctionwith incident photons that carry OAM. At room temperature, thepopulation of vibrationally excited states is small. Stokes-shiftedscattering events shown in FIG. 68 are typically observed in Ramanspectroscopy since at room temperature the excited vibrational statesare low and the electron originates in the ground state. The inelasticRaman scattered photon 6802 has lower energy than the incident photon6804 as the electron decays to an energy level 6806 higher than theoriginal ground state 6808. Anti-Stokes shifted scattering events 6810result from a small fraction of molecules originally in vibrationallyexcited states (FIG. 68) which leave them in the ground state 6812 andresults in Raman scattered photons with higher energy. At roomtemperature, anti-Stokes shifted Raman spectra are always weaker thanStokes-shifted spectrum since the Stokes and anti-Stokes spectra containthe same frequency information. Most Raman spectroscopy focusesexclusively on Stokes-shifted scattering phenomena for this reason.

The force constant by which the vibrational mode energy may be modeledis affected by molecular structure including atomic mass, molecularspecies, bond order, and the geometric arrangement of molecules.However, Raman scattering occurs when the polarizability of moleculesmay be affected.

The polarizability, a, of a molecule appears as a proportionalityconstant between the electric field and the induced dipole moment,P=αE.

The induced dipole scatters a photon at the frequency of the incidentphoton (Rayleigh scattering). Molecular vibration, however, may changethe polarizability and give rise to inelastic Raman scattering ofphotons. Changes in polarizability may be expressed by

$\frac{\partial\alpha}{\partial Q} \neq 0$where Q is in a direction normal to the vibration, and is considered aselection rule for Raman-active vibrations.

Raman-active vibrations are non-existent in the infrared for moleculeshaving a center of symmetry while the existence of a perturbed symmetrycenter (e.g. permanent dipole moment) indicates the absence ofinfrared-active vibrations.

The intensity of a Raman band is proportional to the square of thespatial change of polarizability, or the induced dipole moment,

$I_{Raman} \propto {( \frac{\partial\alpha}{\partial Q} )^{2}.}$Hence, incident photons that slightly induce a dipole moment will yielda Raman band with a very small intensity. Stronger Raman scatteringsystems are those with higher values of α such as molecules havingdouble carbon bonds which exhibit more broadly distributed electronssusceptible to polarization. Subsequently, the range of chemicalconcentrations measurable by Raman spectroscopy is considerably widegiven that the scattering intensity is directly proportional toconcentration.

Raman spectroscopy exhibits several advantages over other spectroscopytechniques. Raman bands exhibit good signal-to-noise ratios owing to itsdetection of fundamental vibrational modes. Hence, the Raman signatureof measured samples is typically more pronounced and definitive.

Raman spectroscopy is more useful for analyzing aqueous solutions thaninfrared spectroscopy since the Raman spectrum of water is weak andunobtrusive while the infrared spectrum of water is very strong and morecomplex. In organic and inorganic chemistries, the existence of covalentbonds yields a unique Raman signature. A Raman spectroscopy setup onlyrequires an appropriate laser source incident on a material and adetector to collect scattered photons which minimizes the need forelaborate sample preparation. Raman spectroscopy is non-destructive asthe material is merely illuminated with a laser. Because the Ramaneffect is weak, the efficiency and optimization of a Raman spectroscopyinstrument is critically important to providing measurements of theslightest molecular concentrations within the shortest possible time.

Spontaneous Raman Spectroscopy

The intensity of spontaneous Raman scattering is linearly dependent onthe incident intensity of light but of several orders of magnitude lessintense. Treating the light-matter interaction quantum mechanically, thetotal Hamiltonian may be expressed in terms of the energy associatedwith the vibrational modes of the molecule, H_v, the light, H_γ, andtheir interaction, H_vγ,H=H_v+H_γ+H_vγ.In this frameworkH_v=½m(p^2+ω_0^2q^2)with vibrational frequency ω_0 and the normal mode amplitude q which maybe expressed in terms of creation and annihilation operators of themolecular vibrations,q=√(2π

/(8π^2μω_0))[b^†+b]with the electric dipole moment μ. This leavesH_v=

ω_0(b^†b+½).

Using creation and annihilation operators for light, a″ t and a, fieldquantization is obtained,E_λ=√((2πhv_L)/(εV_int))Σ_(k_λ)

e_(k_λ)i[ak_λ^†−ak_λ]

where e_(k_λ) is the field polarization unit vector field and Vint theinteraction volume. The Hamiltonian for the light is thenH_γ=Σ_(k_λ)

ω_(k_λ)(a_(k_λ)^†a_(k_λ)+½)

.Using the first order perturbation of the electric dipole approximationthe interaction Hamiltonian may be obtained in terms of the molecule'spolarizability, α,(H_int&=&“E”·α·“E”@&=&“E”·α_0·“E”+(∂α/∂q)_0“E”·q·“E”+ . . . )within the local coordinate system, q. The first term characterizesRayleigh scattering. The remaining first order Raman scattering term isneeded to characterize spontaneous Raman scattering including thecoherent laser field, “E”_L, in addition to the Stokes and anti-Stokesfields, “E”_S and “E”_AS, respectively. Substituting q and E_γ into thisexpression yields

${\bullet( {{{H_{—}{int}}\&} = {{{{{{\& H_{—}\gamma\; S} + {H_{—}\gamma\;{{AS}@}}}\&} \sim}\&}( {{\partial\alpha}\text{/}{\partial q}} )_{—}0\mspace{14mu}{\Sigma_{—}( {k_{—}S\mspace{14mu} k_{—}L} )}\mspace{14mu} \sqrt{}( {( {2\omega_{—}L\mspace{14mu}\omega_{—}s} )\text{/}\omega_{—}0} ) \mspace{14mu}( {{e_{—}( {k_{—}L} )}^{''} \cdot^{''}{e_{—}( {k_{—}s} )}} )( {{{a_{—}( {k_{—}S} )}^{\bigwedge}\dagger\; b^{\bigwedge}\dagger\;{a_{—}( {k_{—}L} )}^{''}} +^{''}{{a_{—}( {k_{—}S} )}\mspace{14mu}{{ba}_{—}( {k_{—}L} )}^{\bigwedge}\dagger}} ){\delta( {{k_{—}L^{''}} -^{''}{k_{—}S^{''}} -^{''}{k_{—}v}} )}}} )} + {( {{\partial\alpha}\text{/}{\partial q}} )_{—}0\mspace{14mu}{\Sigma_{—}( {k_{—}{AS}\mspace{14mu} k_{—}L} )} \sqrt{}( {( ( {2\omega_{—}L\mspace{14mu}\omega_{—}{AS}} ) )\text{/}\omega_{—}0} ) ( {{e_{—}( {k_{—}L} )}^{''} \cdot^{''}{e_{—}( {k_{—}{AS}} )}} )( {{{a_{—}( {k_{—}{AS}} )}^{\bigwedge}\dagger\;{{ba}_{—}( {k_{—}L} )}^{''}} +^{''}{{a_{—}( {k_{—}{AS}} )}b^{\bigwedge}\dagger\;{a_{—}( {k_{—}L} )}^{\bigwedge}\dagger}} ){\delta( {{k_{—}L^{''}} -^{''}{k_{—}{AS}^{''}} +^{''}{k_{—}v}} )}}$where H_γS and H_γAS are the interaction Hamiltonians of the Stokes andanti-Stokes branches, respectively.

The steady state transition rate between the initial, |i

, and final, |f

states is given according to Fermi's golden rule,W_(i→f)=2π/

|

f|H_int|i

|^2ρ(

ω_f).In the simple harmonic oscillator picture, the eigenstates, |n_v

with excitation quanta n_v are acted upon by creation and annihilationoperators to yield the Stokes and anti-Stokes transition ratesW_(n_v)→n_v+1,“and”W_(n_v)→n_v−1˜n_v.Hence, it is easy to determine n_v from the Raman signal intensity givena linear dependence.

Raman intensities from each vibrational level are used to identifyunique vibrational molecular modes and characterize the material'scomposition

The integrated anti-Stokes intensity of a Raman mode is proportional tothe average vibrational quantum number of the mode,

n_v

,I_AS=A(E_R/(hv_R))=A

n_v

where A is the Raman cross section. Normalizing I_AS with respect to theroom temperature Stokes signal of the same mode in addition to using theBoltzmann distribution,

n_v

_0=(E_R^0)/(hv_R)=1/(e^((hv_R)/(kT_0))−1)where E_R^0 is the room temperature (T_0) energy of the Raman mode.Generally, hv_R>>kT_0. so

n_v

_0=0, and the normalized anti-Stokes signal is approximately

n_v

,I_norm≡I_AS/(I_R^0)=A

n_v

/A(1+

n_v

_0)≈

n_v

.By comparing the normalized scattering intensities associated withdifferent vibrational moved, the distribution of energy over differentmolecular modes after infrared excitation may be obtained.Stimulated Raman Spectroscopy

Stimulated Raman intensity is nonlinearly dependent on the incidentintensity of photons but of similar magnitude. Inelastic scattering of aphoton with an optical phonon originating from a finite response time ofthe third order nonlinear polarization of a material is characteristicof Raman scattering. Monochromatic light propagating in an opticalmaterial yields spontaneous Raman scattering in which some photons aretransitioned to new frequencies. The polarization of scattered photonsmay be parallel or orthogonal if the pump beam is linearly polarized.Stimulated Raman scattering occurs when the scattering intensity ofphotons at shifted frequencies is enhanced by existing photons alreadypresent at these shifted frequencies. Consequently, in stimulated Ramanscattering, a coincident photon at a downshifted frequency receives again which may be exploited in Raman amplifiers, for example, orusefully employed in molecular spectroscopy.

Stimulated Raman scattering (SRS) has been observed in glass fibers andRaman gain has been measured in single mode fibers. Raman amplificationbecame a mature technology with the availability of sufficientlyhigh-power pump lasers.

Within a classical electromagnetic framework, the stimulated Ramanscattered signal intensity increases proportionally with the pump andsignal intensities(dI_s)/dz=g_R I_P I_Sand the Raman-gain coefficient, g_R, which is related to the spontaneousRaman scattering cross section. Hence, the probability of Ramanscattering is directly related to the photon density in the pump waveand the Raman cross section.

The Stokes and pump waves must overlap spatially and temporally togenerate stimulated emission. Since, the Raman process involvesvibrational modes of molecules within a material; its intensity spectrumdetermines the material composition. In amorphous materials, forexample, the vibrational energy levels tend to merge and form bands andthe pump frequency may differ from the Stokes frequency over a widerange. In crystalline materials, however, the intensity peaks tend to bewell-separated as they have narrow bandwidths.

The coupled wave equations for forward Raman scattering include(dI_S)/dz=g_RI_pI_S−α_SI_Sfor Stokes intensities with α_S the Stokes attenuation coefficient, and(dI_P)/dz=−ω_P/ω_Sg_RI_pI_s−α_PI_Pfor pump wave intensities where ω_P and ω_S are pump and Stokesfrequencies, respectively. For backward scattering, dI_S/dz→−dI_S/dz. Inthe absence of loss, these expressions reduce tod/dz(I_S/ω_s+I_P/ω_P)=0which embodies the conservation of photon number in Stokes and pumpwaves during stimulated Raman scattering processes.

Stimulated scattering intensity increases when the stimulated gainexceeds the linear loss which is the source of the threshold power whichmust be overcome to initiate stimulated Raman scattering. In a materialsystem in which forward and backward scattering occurs, a beat frequencydrives molecular oscillations responsible for increasing the scatteredwave amplitude. In turn, the increasing wave amplitude enhances themolecular oscillations as part of a positive feedback loop that resultsin the stimulated Raman scattering effect. For forward scatteringprocesses, the pump depletion term is removed,(dI_P)/dz=−α_pI_P.

Solving this equation yields I_P (z)=I_0 e^(−α_P z) giving thestimulated Stokes scattering intensityI_S(L)=I_S(0)e^(g_RI_oL_eff−α_PL)where the effective optical path length is given byL_eff=(1−e^(−α_pL))/α_P.

Stimulated Raman scattering intensifies from scattering events occurringthroughout the optical path length in the material, making it a usefulmolecular spectroscopy technology.

Resonance Raman Spectroscopy

The Raman effect in classical Raman spectroscopy depends only on thefrequency of incident light with scattered intensity dependence on v_0^4as discussed earlier. If the vibrational mode of a molecular absorptiontransition precisely matches the energy of incident light, the observedscattered intensity may be as intense as ˜v_0^6. This resonance Ramaneffect permits highly sensitive spectroscopic discrimination of amolecular species within a complex material medium such as chromophoreswithin proteins embedded in a biological membrane.

In resonance Raman spectroscopy, only a small fraction of molecularvibrational modes are enhanced. In the simplest scenario, only oneelectronic state may be resonant. In this case, the resonant Ramansignal is the result of nuclear motion resulting from distortions of themolecule while transitioning between the ground state and the excitedstate in which resonance is induced by incident light.

The functional component of most biological chromophores consist ofatoms conjugated with the particular electronic transition to whichresonance Raman spectroscopy is selectively sensitive. The frequency ofmeasured resonance Raman bands yields information about the vibrationalstructure of the electronic states involved in the transition used forinducing the resonance. The scattering intensities provide informationabout the nature of mode coupling with the electronic transition.

Raman Effect in Vortex Light

A molecule in vibronic state m subjected to a plane-polarized incidentlight of frequency v_0 and intensity I_0 is perturbed into a newvibronic state n. This interaction causes the frequency of light toshift by v_mn=v_m−v_n and scatter with a frequency v_0+v_mn through asolid angle 4π. The scattering intensity during the transition from m ton is given byI_mn=(2 ^6 π^4)/(3c^3)(v_0+v_mn)^4|

_mn|^2in which the amplitude

_mn of the electric field is given by

_mn=1/hΣ_r

((M_m(M_mr

))/(v_rm−v_0)+(M_mr(M_rn

))/(v_rn+v_0))where, m, r and n are quantum numbers of the initial, intermediate andfinal energy states E_m, E_r, E_n, respectively.

Between the amplitude U of the electric field strength

=

e_^(−2πiv_0t)+

^*e^(2πiv_0t)and its amplitude

_mn associated with the shifted scattered radiation induced torque,M_mn=

_mn e^(−2πi(v_0+v_mn)t)+

_mn^*e^2πi(v_0+v_mn)tis a tensor relation that may be expressed in terms of scattering tensorA_mn=(α_ρσ)_mn in the form

_mn=A_mn

or in component representation,(

_ρ)_mn=Σ_σ

(α_ρσ)_mn

_σ

while the scattering tensor A_mn may be expressed asA_mn=1/hΣ_r

((M_rn M_mr)/(v_rm−v_o)+(M_mr M_rn)/(v_rn+v_0))

,

Since

_mn written in terms dyadic components of the tensor A_mn includes M_rnM_mr, each path matrix element of the polarizability tensor, α, for atransition from m to n, may be written in terms of intermediate vibronicstates

(α_(—)ρσ)_(—)mn = 1/2πΣ_(—)r(((M_(—)ρ)_(—)rn  (M_(—)σ)_(—)mr)/(v_(—)rm − v_(—)0) + ((M_(—)ρ)_(—)mr  (M_(—)σ)_(—)rn)/(v_(—)rn + v_(—)0)),Where (M_ρ)_mn is the transition matrix between vibrational levels m andn in the presence of the radiation operator m^_ρ,(M_ρ)_mn=∫Ψ_r^*m^_ρΨ_m dτ

Herein, (M_l)_rn (M_σ)_mr are ordinary products of scalar vectorcomponents) (M_l)_rn and (M_σ)_mr of a unit vector α_σ. In the threemutually perpendicular directions spatially fixed l, σ=1,2,3 as follows

| — ⁢ mn ⁢ | ⋀ ⁢ 2 = Σ — ⁢ ρ ⁢ ⁢ ⁢ ( — ⁢ l ) — ⁢ mn ⋀ ⁢ 2 = Σ — ⁢ ρ ⁢ ⁢ | Σ — ⁢ σ ⁢ ⁢ ⁢ (α — ⁢ σρ ) — ⁢ mn ⁢ — ⁢ σ ⁢ ⁢ | ⋀ ⁢ 2 = A ⋀ ⁢ 2 ⁢ ⁢ Σ — ⁢ ρ ⁢ | Σ — ⁢ σ ⁢ ⁢ ⁢ ( α — ⁢ ρσ) — ⁢ mn ⁢ ⁢ 𝒶 — ⁢ σ ⁢ ⁢ | ⋀ ⁢ 2 ⁢ ⁢With an incident intensity, I_0=(c/2π)A^2, then,

I_(—)mn = (2^(⋀)6  π^(⋀)4  A^(⋀)2)/(3c^(⋀)3)  (v_(—)0 + v_(—)mn)^(⋀)4  Σ_(—)ρ|Σ_(—)σ(α_(—)ρα)_(—)mn  𝒶_(—)σ|_(⋀)2 = (2^(⋀)7  π^(⋀)5)/(3c^(⋀)3)  I_(—)0  (v_(—)0 + v_(—)mn)^(⋀)4  Σ_(—)ρ|Σ_(—)σ(α_(—)ρσ)_(—)mn  𝒶_(—)σ|_(⋀)2.

The total scattering intensity is therefore dependent on the state ofpolarization of the exciting light. By averaging over all positions ofa, or averaging over all modes of the scattering molecule at a fixedincident wave direction and polarization,(|Σ_σ

(α_ρσ)_mnα_σ

|^2)⁻=⅓Σ_σ

|(α_ρσ)|^2.

Finally, for an electron transition from m→n per molecule an averagetotal intensity of the scattered radiation is obtainedI_mn=(2^7π^5)/(3^2c^4)I_0(v_0+v_mn)^4Σ_(ρ,σ)

|(α_ρσ)_mn|^2in which ρ=x, y, z and σ=x^′, y^′, z′ are independently the fixedcoordinate systems of the molecule for incident and scattered photons,respectively.Selection Rules for Raman Effect Using Vortex Light

Of interest to studies of the Raman effect using vortex light is aparticular set of solutions of Maxwell's equations in a paraxialapproximation. Laguerre-Gaussian functions may mathematicallycharacterize a beam of vortex light in terms of generalized Laguerrepolynomials, L_p^

(x), with a Gaussian envelope. In the Lorentz-gauge, the vectorpotential of a Laguerre-Gaussian beam is

${{A\_}( {\ell,p} )} = {{A\_}0( {{\alpha\;\hat{e}{\_ x}} + {\beta\;\hat{e}{\_ y}}} ) \sqrt{}( {2\;{{p!}/{{\pi( {{\ell } + p} )}!}}} ) {w\_}{0/{w(z)}}\mspace{14mu}{L\_{LP}}^{\bigwedge}{\ell }\mspace{14mu}( {( {2\;\rho^{\bigwedge}2} )/( {w^{\bigwedge}2(z)} )} )( {( { \sqrt{}2 \;\rho} )/{w(z)}} )^{\bigwedge}{\ell }{e^{\bigwedge}( {{i{\ell\phi}} - {i\;\omega\; t} + {ikz}} )}}$in a (ρ, ϕ, z) coordinate system in which w(z) is the beam waist(radius) at which the radial field amplitude goes to 1/e. Forsimplicity, only p=0 is typically chosen. In the dipole approximation,the term, e^ikz is negligible, so the radiation operator of aLaguerre-Gaussian beam may be expressed as

${\hat{m}{\_\rho}} = {{\lbrack {{A\_}0( {{\alpha\;\hat{e}{\_ x}} + {\beta\;\hat{e}{\_ y}}} ) \sqrt{}( {{1/{\pi!}}( {{\ell }!} )\mspace{14mu}{w\_}{0/{w(z)}}\mspace{14mu}{L\_}0^{\bigwedge}i\;\hslash\mspace{14mu}{( {2\;\rho^{\bigwedge}2} )/w^{\bigwedge}}2(z)} ) ( {( { \sqrt{}2 \;\rho} )/{w(z)}} )^{\bigwedge}i\;\hslash\;{e^{\bigwedge}( {{{il}\;\phi} - {i\;\omega\; t}} )}} \rbrack \cdot p} + {c.c}}$Here, e^iωt is associated with photon emission and e^(−iωt) isassociated with photon absorption.

The following generalized framework for developing a set of selectionrules to measure unique OAM Raman signatures of different materialsapplies to the intensity profiles associated with both stimulated andspontaneous Raman spectroscopy.

The relationship among irreducible representations of the phonon, theincident photon, and the scattering photon, Γ_α, Γ_ρ, and Γ_σ, requiredto ensure non-vanishing matrix elements of A_(l,p) isΓ_α⊗Γ_ρ⊗Γ_σ

Γ_1such that h_(e,s)^a, (M_ρ)_(g,e), and (M_σ)_(g,s) are non-zero.Introducing, the Raman tensor P_αβγδ (Γ_j^σ) having index Γ_j^σ todenote the jth branch of the σth phonon to replace the single index a,we similarly replace the incident photon index, ρ, with (α,β) and thescattered photon index, σ with (γ,δ).

As the interaction of light with matter in Raman scattering processesleaves the orbital angular momentum of photons unperturbed the incidentand scattered photons may be expressed in the following respectiveforms,(ρ·∈_1)p^le^ilϕ “and” (ρ·∈_s)ρ^le^(−ilϕ).Then P_αβγδ (Γ_j^σ) may be determined by the Clebsch-Gordan coefficientsfor all three representationsP_(z,∈_s,∈_I,z)(Γ_j^σ)=(ρ·∈_S)ρ^le^(−ilϕ)⊗(ρ−∈_I)p^le^ilϕ⊗ϕ_σ^j

For crystalline materials, the special case of forward scatteringreduces 3×3 Raman tensors to 2×2. In this case, the Raman tensors forl≥2 excitations all have the same form. So from symmetry considerations,the i-dependence vanishes for l≥2. Since the constants a, b, c, d, and edepend on l and the symmetry of the crystal, non-zero OAM yields a Γ₂phonon for l≥2 photon excitation and decouples the two Raman tensors forthe Γ₃ phonon for l≥1 photon excitation.

OAM Raman spectroscopy exhibits the capacity to characterize the atomicand molecular composition of a crystalline material. More complicatedselection rules are needed to fully obtain an OAM Raman signature ofchiral materials which present their own unique atomic and molecularsymmetry properties.

In the highly symmetric case of crystalline materials, for example, theapproach is rather straightforward. Given a periodic lattice potential,electrons in crystal solids may be expressed as Bloch wavesψ_(n,k)(r)=e^(ik·r)u_nk(r)such that the electron transition moment connecting the ground state,ψ_(g,k), to the excited state, ψ_(L)(e,k), may be writtenM_(g,e)=Σ_k

∫

ψ_(e,k)^*(r)[A_0(ρ^le^ilϕ)·p]ψ_(g,k)(r)dr

.The first order Taylor expansion with l=0 is then

(M̂_ρ)_(g, e) = (M̂_ρ)_(g, e)^(⋀)0 + Σ_(α, S)(h_es^(⋀)α Q_a)/(Δ E_(e, S))(M̂_ρ)_(g, e)^(⋀)0.

Since h_(e,S)^α, Q_α, and ΔE_es depend only on the properties of thecrystal and not l, only M affects scattering intensities when usingvortex light. Subsequently, the electronic wavefunction and l are leftas relative values of M(l≠0) with respect to M(l=0) for the Raman effectwith vortex light interactions with crystal solids.

Raman scattering intensity enhancements may be identified by selectingappropriate values of l such as in the case of zinc blende crystals, forexample, in which a maximum was reported for l=30 based on symmetryconsiderations using the approach presented above. In practice, focusinga laser producing vortex light has little impact on the intensityenhancement of M given its similarity to focusing light in an ordinaryRaman scattering measurement.

Polarized Raman Spectroscopy

Given that the polarizability of molecules varies spatially with respectto the distribution of molecules in a sample, a plane-polarized Ramansource may be used to characterize the atomic structure of crystals andmolecular structure of polymeric films, crystals, and liquid crystals.

Referring now to FIG. 69, polarized Raman techniques involve a polarizer6906 between the sample 6904 and the spectrometer 6908 oriented eitherparallel (∥) or perpendicular (|) to the polarization state of the lasersource 6902. As well, polarizing optics 6910 may be inserted between thelaser 6902 and sample 6904 to select an appropriate state ofpolarization incident on the sample.

The symmetry properties of bond vibrations in a molecule arecharacterized by polarized Raman spectroscopy by evaluating thedepolarization, p, of particular intensity peaks,

$\rho = \frac{I_{\bot}}{I_{\parallel}}$where I_⊥ and I_∥ are the Raman spectral band intensities withpolarizations perpendicular and parallel, respectively, to the state ofpolarization of the laser source 6902.

As shown in FIG. 70, information gained by polarized Raman spectroscopy7002 can be used to supplement atomic and molecular information gainedby non-polarized Raman spectroscopy 7004. A single integratedspectroscopy unit 7006 exploiting both polarized and non-polarized Ramaneffects using combined results processing 7008 that improves overallquality and amount of information gained by spectroscopically processingdata from a sample using multiple types of spectroscopic analysis.

Raman Spectroscopy with Optical Vortices

The typical Raman source is a Gaussian laser operating in itsfundamental mode with an electric field

${E( {x,y,z} )} = {\hat{e}E_{0}{\exp( {- \frac{x^{2} + y^{2}}{w^{2}}} )}{{\exp\lbrack {- {i( {{kz} - {\omega\; t}} )}} \rbrack}.}}$traveling in the z-direction, where ê is the polarization vector. Lightproduced by such a source has either linear or circular polarizationwhich are limited to the transverse (x,y) plane with no electric fieldcomponent in the z-direction. The induced dipole moments of interestthen are only P_(x) and P_(y).

A longitudinal mode along the z-direction incident on a moleculescatters light that completes the picture of the molecule'spolarizability to include P_z. An electric field having a z-component isa radially-polarized beam with a polarization vectorê=x{circumflex over (x)}+yŷ={circumflex over (r)}.

Several methods exist to generate radially polarized fields havinglongitudinal components when tightly focused. In Raman spectroscopy, theinduced dipole moment, P_(z), is the result of E_(z) which may increasethe strength of vibrational modes in addition to generating newvibrational modes previously unobserved with conventional Ramanspectroscopy. As shown in FIG. 71, information gained by Raman beamsendowed with optical vortices 7102 adds a third degree of spectroscopiccapability when coupled with polarized 7104 and non-polarized 7106 Ramanspectroscopy in a combined analysis 7108. Such Raman spectroscopy canalso work in conjunction with incident photons that carry OAM.

THz Spectroscopy

Terahertz spectroscopy is conducted in the far-infrared frequency rangeof the electromagnetic spectrum (FIG. 61) and is therefore useful foridentifying far-infrared vibrational modes in molecules. THzspectroscopy can provide a higher signal-to-noise ratio and widerdynamic range than far-infrared spectroscopy due the use of bright lightsources and sensitive detectors. This provides for selective detectionof weak inter- and intra-molecular vibrational modes commonly occurringin biological and chemical processes which are not active inIR-spectroscopy. THz spectroscopy may also be used in conjunction withincident photons that carry OAM. Terahertz waves pass through media thatare opaque in the visible and near-IR spectra and are strongly absorbedby aqueous environments (see FIG. 72).

THz spectroscopy was historically hindered by a lack of appropriatelyhigh powered light sources. However, access to practical THzspectroscopy in the far-infrared range was permitted by the generationof THz rays based on picosecond and femtosecond laser pulses. Today, THzsources include either short pulse mode (e.g. photoconductive antennas,optical rectifiers) or continuous wave (CW) mode having a wide range ofavailable output power (nanowatts to 10 watts).

Several different types of THz sources are used today to interrogatebiological, chemical and solid state processes. Sources in the 1-3.5 THzrange are frequently used in biology and medicine, for example, toinvestigate conformational molecular changes. THz spectroscopy is usedtoday as frequently as Raman spectroscopy.

Terahertz Time-Domain Spectroscopy

Terahertz time-domain spectroscopy (THz-TDS) is one of the most widelyused THz techniques which includes coherent emission of single-cycle THzpulses such as provided by a femtosecond laser. The detection of thesepulses occurs at a repetition rate of about 100 MHz.

Two dimensional THz absorption properties of samples are characterizedby a THz imaging technique. This technique was demonstrated in systemsdesigned for THz-TDS based on picosecond pulses as well as systemsutilizing continuous-wave (CW) sources such as a THz-wave parametricoscillator, quantum cascade laser, or optically pumped terahertz laser.THz spectroscopy can be used in conjunction with incident photons thatcarry OAM.

THz pulse imaging provides broad image frequency information between0.1-5 THz while THz CW imaging may be performed in real-time, isfrequency-sensitive, and has a higher dynamic range due to significantlyhigher spectral power density. In both pulse and CW THz imaging thecharacteristics of the light source (coherency, power, and stability)are important. A THz spectrometer may mechanically scan a sample in twodimensions, but the time of each scan scales with sample size. Real timeTHz imaging is often conducted with an array of THz wave detectorscomposed of electro-optic crystals or a pyroelectric camera. Such THzspectroscopy can be used in conjunction with incident photons that carryOAM.

THz imaging suffers from poor resolution as estimated in terms of itsdiffraction limit which is less than a millimeter and from lowtransmission through an aperture resulting in low sensitivity. To exceedthe diffraction limitation near-field microscopy is used to achievesub-wavelength resolution, though low transmission remains an issue.

Fluorescence Spectroscopy

Perturbed by incident light, electrons in molecules at room temperatureare excited from the lowest vibrational energy level 7302 of theelectronic ground state to either the first (S_1) 7304 or second (S_2)7306 vibrational state (FIG. 73) and may occupy any one of severalvibrational sub-levels. Each vibrational sub-level has many neighboringrotational energy levels in such close proximity that inter-sub-levelenergy transitions are almost indistinguishable. Consequently, mostmolecular compounds have broad absorption spectra with the exception ofthose having negligible rotational characteristics such as planar andaromatic compounds.

In fluorescence spectroscopy, molecules absorb energy from incidentphotons, obtain a higher vibrational energy sub-level of an excitedstate (S_1 or S_2), then lose their excess vibrational energy throughcollisions and return to the lowest vibrational sub-level of the excitedstate. Most molecules occupying an electronic state above S_2,experience internal conversion and decay by collision through the lowestvibrational energy sub-level of the upper state to a higher vibrationalsub-level of a lower excited state having the same energy. The electronscontinue to lose energy until they occupy the lowest vibrational energysub-level of S_1 7308. The decay of the molecule into any vibrationalenergy sub-level of the ground state causes the emission of fluorescentphotons.

If the absorption and emission process differs from this sequence, thequantum efficiency is less than unity. The “0-0” transition from thelowest vibrational ground state sub-level to the lowest vibrational S_1sub-level 7308 is common to both the absorption and emission phenomenawhile all other absorption transitions occur only with more energy thanany transition in the fluorescence emission. The emission spectrumsubsequently overlaps the absorption spectrum at the incident photonfrequency corresponding to this “0-0” transition while the rest of theemission spectrum will have less energy and equivalently occurs at alower frequency. The “0-0” transition in the absorption and emissionspectra rarely coincide exactly given a small loss of energy due tointeraction of the molecule with surrounding solvent molecules.

Hence, distributions of vibrational sub-levels in S_1 and S_2 are verysimilar since incident photon energy doesn't significantly affect theshape of the molecule. Energy differences between bands in the emissionspectrum will be similar to those in the absorption spectrum andfrequently, the emission spectrum will be approximately a mirror imageof the absorption spectrum. The shape of the emission spectrum is alwaysthe same despite an incident photon frequency shift from that of theincident radiation since the emission of fluorescent photons alwaysoccurs from the lowest vibrational energy sub-level of S_1. If theincident radiation intensity yielding excitation remains constant as thefrequency shifts, the emission spectrum is considered a correctedexcitation spectrum.

The quantum efficiency of most complex molecules is independent of thefrequency of incident photons and the emission is directly correlated tothe molecular extinction coefficient of the compound. In other words,the corrected excitation spectrum of a substance will be the same as itsabsorption spectrum. The intensity of fluorescence emission is directlyproportional to the incident radiation intensity.

Fluorescence spectroscopy results in emission and excitation spectra. Inemission fluoroscopy, the exciting radiation is held at a fixedwavelength and the emitted fluorescent intensity is measured as afunction of emission wavelength. In excitation fluoroscopy, the emissionwavelength is held fixed and the fluorescence intensity is measured as afunction of the excitation wavelength. This type of fluorescencespectroscopy may also be used in conjunction with incident photons thatcarry OAM. Performing both emission and excitation spectra togetheryields a spectral map of the material under interrogation. Materials ofinterest may contain many fluorophores, and different excitationwavelengths are required to interrogate different molecules as shown inFIGS. 74A and 74B for the absorption and emission spectra fortryptophan, elastin, collagen, nicotinamide, adenine dinucleotide (NADH)and flavins.

Fluorescence spectrometers analyze the spectral distribution of thelight emitted from a sample (the fluorescence emission spectrum) bymeans of either a continuously variable interference filter or amonochromator. Monochromators used in more sophisticated spectrometersselect the exciting radiation and analyze the sample emission spectra.Such instruments are also capable of measuring the variation of emissionintensity with exciting wavelength (the fluorescence excitationspectrum).

One advantage of fluorescence spectroscopy compared to equivalentabsorption techniques is that the sample may be contained in simple testtubes rather than precision cuvettes without appreciable loss inprecision because of the geometrical configuration of simplefluorimeters in which only the small central region of the cuvette isinterrogated by the detector. Hence, the overall size of the cuvette isless important.

Sensitivity of fluorescence spectroscopy depends largely on theproperties of the measured sample and is typically measured in parts perbillion or trillion for most materials. This remarkable degree ofsensitivity permits reliable detection of very small sample sizes offluorescent materials (e.g. chlorophyll and aromatic hydrocarbons).

Fluorescence spectroscopy is exceptionally specific and less prone tointerference because few materials absorb or emit light (fluoresce) andrarely emit at the same frequency as compounds in the target material.

Fluorescence measurements scale directly with sample concentration overa broad frequency range and can be performed over a range ofconcentrations of up to about one six orders of magnitude without sampledilution or alteration of the sample cell. Additionally, the sensitivityand specificity of fluoroscopy reduces or eliminates the need for costlyand time-consuming sample preparation procedures, thus expediting theanalysis. Overall, fluoroscopy represents a low-cost materialidentification technique owing to its high sensitivity (small samplesize requirement).

Pump-Probe Spectroscopy

Pump-probe spectroscopy is used to study ultrafast phenomena in which apump beam pulse perturbs atomic and molecular constituents of a sampleand a probe beam pulse is used to interrogate the perturbed sample afteran adjustable period of time. This optical technique is a type oftransient spectroscopy in which the electronic and structural propertiesof short-lived transient states of photochemically or photophysicallyrelevant molecules may be investigated. The resulting excited state isexamined by monitoring properties related to the probe beam includingits reflectivity, absorption, luminescence, and Raman scatteringcharacteristics. Electronic and structural changes occurring withinfemto- to pico-second timeframes may be studied using this technique.

Generally, pump-induced states represent higher energy forms of themolecule. These higher energy molecular forms differ from their lowestground state energy states including a redistribution of electronsand/or nuclei.

A basic pump probe configuration is shown schematically in FIG. 75. Apulse train generated by a laser 7502 is split into a pump pulse 7506and a probe pulse 7508 using a beamsplitter 7504. The pump pulse 7506interacts with the atoms and molecules in a sample 7510. The probe pulse7508 is used to probe the resulting changes within the sample after ashort period of time between the pulse train and the probe pulse train.By changing the delay time between pulse trains with an optical delayline, a spectrum of absorption, reflectivity, Raman scattering, andluminescence of the probe beam may be acquired after the sample to studythe changes made by the pump pulse train at detector 7512. It ispossible to obtain information concerning the decay of the pump-inducedexcitation by monitoring the probe train 7508 as a function of therelative time delay. The probe train 7508 is typically averaged overmany pulses and doesn't require a fast photodetector 7512. The temporalresolution of measurements in pump-probe spectroscopy is limited only bythe pulse durations of each train. In general, the uncertainty in timingmust be smaller than the timescale of the structural or electronicprocess induced by the pump train.

In two-color pump-probe spectroscopy, the pump 7506 and probe 7508 beamshave different wavelengths produced by two synchronized sources. Whilethis technique provides additional capabilities in ultrafastspectroscopy, it's essential to ensure precise source synchronizationwith a very low relative timing jitter.

In comparison with spontaneous Raman scattering intensities, thescattered intensities provided by a pump-probe Raman spectroscopytechnique may be tremendously enhanced with different pump and probefrequencies, Ω and ω, as shown in FIG. 76. The frequency of the pumpbeam is changed, while the frequency of the probe beam is fixed. Thepump beam is used to induce Raman emission, while the probe beam servesto reveal Raman modes. Both the pump and the probe beam traverse aRaman-active medium in collinearity. When the difference between thepump and probe frequencies coincide with a Raman vibrational modefrequency, v, of the medium, the weak spontaneous Raman light isamplified by several orders of magnitude (10-10⁴) due to the pump photonflux. Gain is achieved as shown in FIG. 76.

The pump beam is essentially engineered to provide a variety ofperturbative excitations within a wide range of samples. Pump-probespectroscopy is therefore applicable to use within the context of otherspectroscopy techniques including the use of a pump beam endowed withorbital angular momentum as discussed in the next section.

Orbital Angular Momentum (OAM) Spectroscopy

Chiral optics conventionally involved circularly polarized light inwhich a plane polarized state is understood as a superposition ofcircular polarizations with opposite handedness. The right- andleft-handedness of circularly polarized light indicates its spin angularmomentum (SAM), ±h in addition to the polarization one can use thehelicity of the associated electromagnetic field vectors. Itsinteraction with matter is enantiomerically specific. The combinedtechniques would have specific signatures for different materials.

As described more fully herein above, optical vortices occurring inbeams of light introduce helicity in the wavefront surface of theelectromagnetic fields and the associated angular momentum is considered“orbital”. Orbital angular momentum (OAM) of photonic radiation isfrequently called a “twisted” or “helical” property of the beam. Moststudies of OAM-endowed light interactions with matter involve achiralmolecules.

Delocalized OAM within solid materials associated with the envelopewavefunction in a Bloch framework, which may be spatially macroscopic inextent, may be distinguished from local OAM associated with atoms. Thelatter is associated with the Landé g-factor of electronic states andpart of the effective spin while the former is of interest to orbitallycoherent systems (e.g. quantum Hall layers, superconductors, andtopological insulators). Development of these techniques representsopportunities to improve our understanding of scattering and quantumcoherence of chiral electronic states, with potential implications formaterials discovery and quantum information. To this end, theoreticalframeworks describing the OAM-matter interaction, such as withdielectric materials are useful.

OAM-endowed beams of light have been used to induce such delocalizedOAM-states in solids using a time-resolved pump-probe scheme using LGbeams in which the OAM-sensitive dichroism of bulk n-doped (3×10¹⁶ cm⁻³Si) and undoped GaAs (held in a cryostat at 5K) is exploited. Using thismethod, “whirlpools” of electrons were induced and measured with atime-delayed probe beam whose OAM components were detected in a balancedphotodiode bridge. The study demonstrates that time-resolved OAM decayrates (picoseconds to nanoseconds) are doping dependent, differed fromspin and population lifetimes, and longer than anticipated as describedin M. A. Noyan and J. M. Kikkawa, “Time-resolved orbital angularmomentum spectroscopy,” Appl. Phys. Lett. 107 032406 (2015), which isincorporated herein by reference in its entirety.

A simple pump-probe OAM spectroscopy instrument is shown schematicallyin FIG. 77 in which the OAM pump beam 7702 is an l=±1 Laguerre-Gaussianbeam cycled between l=+1 and l=−1 at some frequency, v_l. The pump beam7702 perturbs target molecules in the sample 7704 while a direct probebeam 7406 is used to interrogate the resulting perturbation. The samplemay be a crystalline solid, amorphous solid, liquid, biological, orinorganic.

The interaction of light exhibiting OAM, an azimuthal photonic flow ofmomentum, with chiral molecules is the subject of several recenttheoretical and experimental reports. On one hand, the strength of theinteraction has been conjectured as negligible, while on the other hand,not only does such an interaction exist, it may be stronger than theinteractions occurring in conventional polarimetry experiments in whichthe direction of linearly polarized light incident on a solution isrotated by some angle characteristic of the solution itself. A fewlimited experimental studies have suggested that the former theoreticalbody of work is correct—that such an interaction is negligible.

Nonetheless, a variety of light-matter interactions involvingOAM-endowed optical beams indicate a broad range of possibilities inspectroscopy including OAM transfer between acoustic and photonic modesin optical fibers, OAM-endowed Raman sideband generation, and themanipulation of colloidal particles manipulation with optical OAM“tweezers”.

OAM Spectroscopy of Chiral Molecules

Recent experiments using Laguerre-Gaussian (LG) beams of varying integerazimuthal order, l, traveling through a short optical path length ofvarious concentrations of glucose, support the theoretical body of worksuggesting the existence of measurable OAM light-matter interactions.These experiments suggest that not only does the interaction exist, butit appears to be stronger than with polarimetry since perturbations ofthe OAM beam occur within a very short optical path length (1-3 cm) thancommonly required in conventional polarimetry studies (>10 cm) to obtaina measureable perturbation of the linear state of polarization.

The Gaussian beam solution to the wave equation and its extension tohigher order laser modes, including Hermite-Gaussian (HG) and commonlystudied in optics labs. Of particular interest, LG modes exhibit spiral,or helical, phase fronts. In addition to spin angular momentum, thepropagation vector includes an orbital angular momentum (OAM) componentoften referred to as vorticity.

A spatial light modulator (SLM) is frequently used to realize hologramsthat modulate the phase front of a Gaussian beam and has renewedinterest in engineered beams for a variety of purposes.

The expression for the electric field of an LG beam in cylindricalcoordinates is

${u( {r,\theta,z} )} = {\lbrack \frac{2\;{pl}}{1 + {\delta_{\sigma,m}{{\pi( {\ell + p} )}!}}} \rbrack^{\frac{1}{2}}\exp{\{ {{j( {{2p} + \ell + 1} )}\lbrack {{\psi(z)} - \psi_{0}} \rbrack} \} \cdot \frac{\sqrt{2}r}{w^{2}(z)}}{L_{p}^{\ell}( \frac{2r^{2}}{w^{2}(z)} )}{\exp\lbrack {{{- {jk}}\frac{r^{2}}{2{q(z)}}} + {i\;\ell\;\theta}} \rbrack}}$

with w(z) the beam spot size, q(z) a complex beam parameter comprisingevolution of the spherical wavefront and spot size, and integers p and lindex the radial and azimuthal modes, respectively. The exp(ilθ) termdescribes spiral phase fronts. A collimated beam is reflected off theSLM appropriately encoded by a phase retarding forked grating, orhologram, like the one shown in FIGS. 15A-15D. The generating equationfor the forked hologram may be written as a Fourier series,

${{T( {r,\varphi} )} = {\sum\limits_{m = {- \infty}}^{\infty}\;{t_{m}{\exp\lbrack {- {{im}( {{\frac{2\;\pi}{D}r\;\cos\;\varphi} - {\ell\;\varphi}} )}} \rbrack}}}},$where r and φ are coordinates, l is the order of vorticity, and D is therectilinear grating period far from the forked pole. Weights, t_m, ofthe Fourier components may be written in terms of integer-order Besselfunctions,t _(m)=(−i)^(m) J _(m)(kβ)exp(ikα).where kα and kβ bias and modulate the grating phase, respectively. Onlya few terms are needed to generate OAM beams, such as −1≤m≤1,

${T( {r,\varphi} )} = {\frac{1}{2} - {\frac{1}{2}{{\sin( {{\frac{2\pi}{D}r\mspace{14mu}\cos\mspace{14mu}\varphi\mspace{14mu}\varphi} - {\ell\varphi}} )}.}}}$

As shown in FIG. 78 for OAM mode orders l=5, 6, and 7 propagated through3 cm cuvettes containing different concentrations of glucose, the OAMsignature was found to be nonlinear with respect to concentration.Though this preliminary data is noisy, the trend persists over severalOAM orders and was repeatable day to day and after several setupre-alignments and other changes made for convenience.

Glucose exhibits a broad optical absorption band at ˜750 nm with FWHM˜250 nm. A stronger OAM response was observed at 543 nm where absorbanceis four times smaller than at 633 nm. This suggests an interaction basedon the real part of susceptibility, χ^′, rather than its imaginary part,χ″. In separate glucose polarimetry experiments with cuvettes as long as20 cm, a 50% larger specific rotation was measured at 543 nm than at 633nm. Consistent with previous OAM polarimetry studies with chiralmolecules in solution no discernable polarization state changes wereobserved with OAM beams through 3 cm or shorter samples.

While glucose is known to have polarimetric responses at thesewavelengths the concentration-path length product, cl, was too small inthis OAM study to produce measureable shifts in the state ofpolarization. The observed topological changes reported usingOAM-endowed beams suggests the interaction of OAM beams with chiralmolecules is more pronounced than interactions associated withtraditional polarimetry. OAM beam interactions with chiral molecules maylead to new metrological techniques and perhaps a richer understandingof subtle light-matter interactions. Of particular interest is theinteraction of light with molecules exhibiting varying degrees ofchirality, a subject taken up in the next section.

Molecular Chirality

The chirality of a molecule is a geometric property of its “handedness”characterized by a variety of spatial rotation, inversion, andreflection operations. Conventionally, the degree of chirality ofmolecules was starkly limited to a molecule being either “chiral” or“achiral” in addition to being “left-handed” or “right-handed”. However,this binary scale of chirality doesn't lend well to detailedspectroscopic studies of millions of molecular systems that may bestudied. In its place, a continuous scale of 0 through 100 has beenimplemented for the past two decades called the Continuous ChiralityMeasure (CCM). Essentially, this continuous measure of chiralityinvolves the Continuous Symmetry Measure (CSM) function,

${S^{\prime}(G)} =  {\frac{1}{n}\sum\limits_{i = 1}^{n}}\;||{P_{i} - {\hat{P}}_{i}} ||^{2}$where G is a particular symmetry group, P_(i) are the points of theoriginal configuration,{circumflex over (P)}_(i) are the correspondingpoints in the nearest G-symmetric configuration, and n is the totalnumber of configuration points.

The objective is to identify a point set, P_(i), having a desiredG-symmetry such that the total normalized displacement from the originalpoint set P_(i) is a minimum. The range of symmetry, 0≤S′(G)≤1, may beexpanded such that S=100S′. The advantages of CCM over other chiralmeasure schemes include its ease of application to a wide variety ofchiral structures including distorted tetrahedra, helicenes, fullerenes,frozen rotamers, knots, and chiral reaction coordinates, as well asbeing a measured without reference to an ideal shape. Unique chiralityvalues are made with reference to nearest symmetry groups (σor S₂), thusallowing for direct comparison with a wide variety of geometric.

Yet, since the new technique described above discusses the use ofStimulated Raman or Resonant Raman spectroscopy with vector beams (i.e.,beams with “twistedness” plus polarization), the technique can equallybe applied to both chiral and non-chiral molecules.

Raman with Orbital Angular Momentum

The effect of orbital angular momentum on the Raman scattering spectraof glucose has been investigated. Changes have been observed in theRaman spectra, in particular at 2950 cm⁻¹ with L=2 (helical beam) ascompared to L=0 (Gaussian beam). The innovation is that if the sugarmolecules possess some types of chiral symmetry 7908 than there may be adifferential signal 7902 (FIG. 79) using OAM 7904 and Raman 7906spectroscopy. The Raman spectra of glucose, sucrose and fructose havealready been collected for the three laser wavelengths 488, 514.5 and632.8 nm from argon-ion and helium neon laser sources, the signals havebeen tabulated and the agreement of each vibration is justified with theother two laser lines. No resonances were observed as would be expectedsince there is no direct electronic absorption with these energies. TheRaman spectra, however, are sensitive to local and global symmetries ofthe molecule at any wavelength. Differential Raman signals will givefundamental information about the interaction of a chiralelectromagnetic field with the sugar molecules, as well as potentiallylead to a selected symmetry resonance for low level glucose detection inthe blood.

The system used for these measurements is a confocal microscope attachedto a 75 cm single stage spectrometer using a grating blazed at 500 nmand 1200 lines/mm groove density. The microscope objective used was 10×magnification. To generate the OAM beam with angular momentum value L=2,a Q plate was incorporated into the system.

Referring now to FIG. 80 there is illustrated the alignment procedure. Alinear polarizer is inserted at step 8002 into the beam path and rotatedat step 8004 until maximum transmission intensity is achieved. A Q-plateis inserted at step 8006 into the beam path and locates at step 8008 thecenter that produces the OAM beam (by observation of the donut). Thecircular polarizer is inserted at step 8010 before the Q-Plate. Thelinear polarizer is placed at step 8012 after the Q-plate to observe the4 lobed structure. Finally, the circular polarizer is rotated at step8014 until the output from final linear polarizer shows donut for allangles of final linear polarization. This procedure is iterative alsoadjusting applied voltage to Q-plate (appx 4 Volts) and the square wavedriving frequency (appx 2 KHz). The measurements are taken without thefinal linear polarizer.

The resulting spectra with L=2 along with a spectra with L=0 (noelements in the beam path) are shown in FIGS. 81 and 82, both normalizedto the maximum value which for both cases is the Raman signal near 2800cm⁻¹. From these measurements it does show that there are differentialintensities between the two different excitations. At 400 and 550 cm⁻¹there is almost a 50 percent increase in scattering intensity while theL=2 spectrum shows a few additional shoulders of each of these lines.Most pronounced is the intensity ratio of the doublet around 2950 cm⁻¹.

The Raman system used for these measurements is alignment restricted.The incorporation of the additional waveplates causes slight walk-offwhich leads to significant collection intensity drop in the confocalsystem. Presumably, normalization would eliminate any alignmentintensity issues, however signal to noise suffers and longerintegrations are required. Long integration times are not alwayspossible or feasible.

These measurements need to be repeated for glucose and also done forfructose. Also needed to be checked is the response to pure circularpolarization without OAM. We should be able to access the alignment andoptimize for the Q-plate operation. Also to do is use L=1 value and L=20values of OAM. With promising results, we will use a quarter waveplatefor 488 nm as this laser produces the best spectra in the shortestacquisition times on the system.

Although the higher energy Raman signals are not unique to glucose asthey represent generic carbon and carbon hydrogen bonds present in manyorganic systems, it may prove to be unique to chiral systems.Additionally, the lower energy modes that are more unique to glucose mayshow better differentiation with OAM once the system is better optimizedfor Q-plates.

Optical Activity with Single Crystal Rock Candy

Optical activity of sugar molecules is well studied and is a result ofthe chiral symmetry of the molecule which leads to the polarization ofthe sugar system imparting a small rotation of the incident light,therefore the final transmitted beam will have a rotation dependent onthe concentration of molecules present. Experiments have been started inorder to develop a versatile and sensitive system for the detection ofpolarization changes via transmission or reflection of materials usingorbital angular momentum. This system is best suited with the use of theSLM so that any type of beam can in principle be generated. As astarting point, we have obtained rock candy which shows highcrystallinity and regular cleavage planes of the samples which are fewmm thick each. These candy samples can be polished to have an opticalquality finish on the surfaces, however interior defects so far haveprevented clean transmission measurements and the signal is collected asforward scatter. The crystals cleave into 3 pieces showing the clearsymmetry of the planes of the crystal, the z-axis of the crystal isoblique to the cleavage planes. As we begin these measurements, we arealso comparing data to the Q-plate outputs as well. This measurementsystem will become the optical system for balanced and lock-in detectionfor future polarization sensitive measurements and the stimulated Ramanmeasurements.

Multiple monitor access is needed for the SLM on properly configuredcomputers capable of running the SLM, Matlab and video capturesimultaneously.

Referring now to FIG. 81, the output of a HeNe laser is chopped around 1kHz and sent into a single mode fiber. The output is collimated with twobiconvex lenses, sent through a half wave plate to adjust thepolarization incident onto the Hamamatsu LCOS SLM 8102 with an angle ofincidence of <10 degrees per operation specifications of SLM. The SLM8102 displays forked diffraction grating or spiral phase patternholograms generated using the MATLAB code in order to generate thedesired OAM beam. The reflected beam carries OAM and a characteristic“donut” shape is seen, with zero intensity along the beam axis. Thisbeam is then sent through a pair of crossed polarizers 8104 and to thedetector 8106 for lock-in detection. We will also explore experimentalsystem which incorporates the use of a balanced detector.

Experiments have shown a shift of approximately 20 degrees in theintensity curve for these polished sugar crystals. A series ofmeasurements are taken once the detection scheme is finalized. Theseinclude:

1. Optical activity through the entire polished crystal.

2. Optical activity through each of the cleaved pieces independently toinvestigate if there is additive/subtractive effects of optical activityfor different cleavage directions and if any of the directions aresensitive to OAM.

Raman Detection of Glycated Protein

Hb and Hb-A1c a proteins by Raman spectroscopy using OAM may also beinvestigated. Mammalian blood is considered as connective tissue becauseof its cellular composition and due to its embryonic origin and also dueto the origin and presence of colloidal proteins in its plasma. RedBlood cells and Plasma proteins are the major constituents of blood.These connective tissue components are targets for metabolic stressunder disease conditions and result in the chemical alterations. All theblood components are subjected to excessive metabolic stress underhyperglycemic states. Blood acts a primary transporter of nutrients,gases and wastes. Blood plasma acts as a primary carrier for glucose tothe tissues. Normal pre-prandial plasma glucose levels are 80 mg/dl to130 mg/dl and normal postprandial plasma glucose is <180 mg/dl. TheRenal Threshold for Glucose (RTG) is the physiologic maximum of plasmaglucose beyond which kidneys fail to reabsorb the glucose and getexcreted in urine. This is a condition called glycosuria. Glycosuria isthe key characteristic of Diabetes mellitus (DM). High plasma glucose inDM will cause increased levels of Glycosylated Hemoglobin also known asHbA1c. Under normal physiological conditions HbA1c levels are <7%, thisalso expressed as eAG which should be below 154 mg/dl in Normo-glycemiccondition.

Glycation of Plasma Proteins in DM

Glycation is defined as the non-enzymatic random nonspecific covalentlinking of glucose or other hexose sugar moieties to the proteins. Undernormal blood glucose levels in healthy individuals will have levels <7%Glycated Hemoglobin (HbA1c) in the blood, however under hyperglycemicconditions like DM, its levels will increase. Higher blood glucoselevels can induce glycation of other major proteins of blood plasma likealbumin.

Advantages of Measurement of Glycated Proteins in DM:

Measurements of blood glucose levels only provide the information aboutthe glycemic status of a subject at a given moment, i.e. a diabeticperson with uncontrolled blood sugar levels for several months may yieldnormal blood glucose level if he/she gets the test under fasting stateor with low carbohydrate intake on a given day. However the measurementof Glycated hemoglobin (HbA1c) levels in blood yield the informationabout average blood sugar levels in patient for past 2 to 3 months.Therefore it has become a standard clinical practice since past decadeto measure Glycated Hemoglobin in patients with DM with the developmentsensitive and reliable laboratory analyses. We propose the use of Ramanspectroscopic studies on Diabetic blood and its components for thedetection of specific Raman finger prints that may result fromnon-enzymatic glycosylation of key blood proteins Hemoglobin, plasmaalbumin and others in its native and altered physical states. Theprocess of glycation in proteins induces the chemical alterations,structural modifications, conformational changes. Any or all of thesecan result in special Raman spectral changes which can used as aclinical marker.

Measurements were carried out with a small benchtop OceanOptics Ramansystem with 532 nm excitation.

Raman Spectroscopy of Tryptophan:

The Hemoglobin (tetramer) has 6 residues of Tryptophan thereforeHemoglobin is a fluorescent protein. Tryptophan can undergo glycationand result in conformational changes in Hemoglobin. The tryptophanchanges can be identified by using Raman studies (Masako Na-Gai et al.Biochemistry, 2012, 51 (30), pp 59325941) which is incorporated hereinby reference. In order to understand the glycation induced Ramanspectral changes in Tryptophan residues Raman spectra is obtained fromanalytical grade amorphous Tryptophan using 532 nm OceanOptics Raman

Raman Spectra of Proteins:

Solid amorphous powders of albumin and Glycated albumin samples weresubjected to Raman measurements using a OceanOptic 532 nm Raman systemand the confocal Raman system using 488, 514.5 and 632.8 nm. No Ramansignal was observed from these samples, and therefore we need to retestin solution at a physiologic pH of 7.4.

The next steps are:

1. NIR Raman: Blood and its components have intense fluorescence invisible range so NIR Raman may help reduce fluorescence and get goodRaman signals from target protein molecules.

2. OceanOptics 532 nm Raman: This can be used detect some of Glycationderivatives in blood. This needs normal and diabetic blood either fromhuman subjects or animal models. And also Reference spectra of syntheticglycation products can be obtained by using this system, which can laterbe compared with the Raman signal from blood samples.

3. In Vivo Animal model: For future experiments to be successful for invivo blood glucose and diabetes testing, the Raman measurements need tobe carried out in a rat diabetes animal model.

OAM with Raman for Food Freshness, Spoilage, and Organic Detection

Another aspect that will be investigated is food safety concerns due tospoilage of meats, produce, diary, and grains and determination iflabeled food is organic using Raman and OAM. Public and individualconcern led to both governmental regulation and commercial requirementsof quality, stability, and safety of food storage periods. Moreover,food deterioration resulting in food spoilage leads to not only healthissues but also economic loss to food manufacturing and relatedindustries. Thus, minimizing food spoilage, determining food freshness,or maximizing shelf life of food is desired.

Moreover, in 2000, the U.S. Department of Agriculture (“USDA”)established guidelines and national standards for the term “organic.”For example, organic food, as defined by USDA guidelines, means thatfood must be produced without sewer-sludge fertilizers, syntheticfertilizers and pesticides, genetic engineering, growth hormones,irradiation, and antibiotics.

The traditional physical characteristics of food spoilage, such asunpleasant smells, unpleasant tastes, color changes, texture changes,and mold growth, manifest well after biochemical processes have occurredthat impair food quality or safety. As a result, they are not adequateindicators of determining acceptable criteria to use for food freshness,preservation, and spoilage.

Thus, research to date includes the identification of so-called“biomarkers” of food spoilage. This research includes identification ofthe biochemical mechanisms that produce certain chemical by-productsthat are associated with the physical characteristics of food spoilage.These mechanisms can be physical (e.g., temperature, pH, light,mechanical damage); chemical (e.g., enzymatic reaction, non-enzymaticreaction, rancidity, chemical interaction); microorganism-based (e.g.,bacteria, viruses, yeasts, molds); or other (e.g., insects, rodents,animals, birds).

One aspect of the investigation is to use OAM and Raman techniques toidentify these so-called biomarkers and their associated concentrationsto better determine shelf life of basic food categories. Additionally,another aspect of the invention is to investigate the chemicals usedthat would fail to qualify foodstuffs as “organic.” For example, theTable 1 below shows several researched biochemical processes andchemical by-products associated with food spoilage mechanisms associatedwith common food groups:

TABLE 1 Food Category/ Biochemical Process Mechanism Spoilage ActionResulting Biomarker Oxidation Light Reversion Flavor of Soybean 2-pentylfuran Oxidation Light Sunlight flavor in milk dimethyl disulfide, 2-butanone, ethanol, diacetyl, n-butanol Oxidation Light Loss ofRiboflavin, Vitamins vitamin D-5, 6 ep25 D, E, and C oxide OxidationLight Greening of Potato alpha-solanine, alpha- chaconine OxidationDecay meat and diary (fats, oils, aldehydes lipids) Enzymatic DecayChicken/Meat dimethylsulfide, dimethyl disulfide, dimethyl trisulfide,dimethyl tetrasulfide, hydrogen sulfide, ethanol, 3-methyl-1-butanol,acetic acid, propanioc acid, methanethiol, free fatty acids (FFAs)Enzymatic: Decay Fruits, Vegatables, Meat, biogenic amines (tyraimine,Decarboxylation of free Fish, Poultry putrescine, cadaverine, aminoacids (natural histamine) fermentation or via contimation ofmicroorganisms) Enzymatic Decay Vegatables (loss of vitamin ascrbicacid, oxidase C) Enzymatic Decay Milk, oils (hydrolytic lipase,glycerol, free fatty rancidity) acids (FFAs), 3-(E)-hexenal, 2-(E)-hexenal Enzymatic Decay Vegatables (loss of vitamin lipoxygenase A)Enzymatic Decay Fruits (loss of pectic petic enzymes substances, i.e.,softing) Enzymatic Decay Fruits (browning) peroxidases (polyphenoloxidase, o-diphenol, monophenol, o-quinone) Enzymatic Decay Fruits,Vegatables melanin (browning, sour flavor, vitamin loss) Enzymatic DecayEggs, Crab, Lobster, Flour proteases (reduction of shelf life,overtenderization, reduction in gluten network formation) EnzymaticDecay Meats, Fish thiaminase Microbial Bacteria Carbohydrates alcoholic(ethanol, CO2); (fermentation) homofermentative lactic acid (lacticacid); heterofermentative lactic acid (lactic acid, acetic aci, ethanol,CO2); propionic acid fermentation (propionic acid, aetic acid, CO2);butyric acid fermentation (butyric acid, acetic acid, CO2, H2); mixedacid fermentation (lactic acid, acetic acid, CO2, H2, ethanol);2,3-butanediol fermentation (CO2, ethanol, 2,3- butanediol, formic acid)Microbial Bacteria Degradation of N- (H2S, methyl mercaptns, Compoundsindole, cadaverine, putrescine, histamine) Microbial bacteria Fish(odor) trimethylamine Microbial Bacteria Lipids aldehyde, ketonesMicrobial Bacteria Pectin Degradation polygalcturonic acid, galacturonicacid, methanol Fishy Odor Decay Meat, Egg, Fish trimethylamine Garlicodor Decay Wine, Fish, Meat, Milk dimethyl trisulfide Onion odor DecayWine, Fish, Meat, Milk dimethyl disulfide Cabbage odor Decay Wine, Fish,Meat, Milk dimethyl sulfide Fruity odor Decay Milk, Fish, Wine estersPotato odor Decay Meat, Egg, Fish 2-methoxy-3- isopropylprazineAlcoholic odor Decay Fruit juices, Mayonnaise ethanol Musty odor DecayBread, Wine tricholoranisole Cheesy odor Decay Meat diacetyl, acetoinMedicinal odor Decay Juice, Wine 2-methoxy phenol Souring Decay Wine,Beer, Dairy acetic acid, lactic acid, citric acid Slime Decay Meat,Juices, Wine polysaccharide Curdling Decay Milk lactic acid Holes DecayHard cheese carbon dioxide

A person skilled in the art would be well aware of various othermechanisms and biochemical indicators evidencing food spoilage of commonfoodstuffs, including other reactions or volatile or non-volatileorganic compound (VOC) by-products associated with food spoilage.Likewise, a person skilled in the art would be well aware of thechemicals and additives that do not qualify food as organic, whetherinvestigating grains, diary, produce, or meats.

Traditional spectroscopy techniques are not adequate to identify inreal-time or adequate concentration these bio-markers in any meaningfulmanner to determine shelf life of the food sample or organic nature ofthe food in question. The present investigation and invention willemploy Raman and OAM techniques described above to classify, identify,and quantify the various bio-markers in the table above and the commonchemicals that do not qualify food as organic as defined in federalregulations.

Such techniques are equally applicable whether the biomarker or chemicalis a chiral or non-chiral molecule. Such data can then be correlated toconcentration of degradation of the sampled food group to determineminimum and maximum concentrations acceptable to food freshness,spoilage, organic quality, and safety.

Ince-Gaussian Spectroscopy

Another type of spectroscopic technique that may be combined with one ormore other spectroscopic techniques is Ince-Gaussian Spectroscopy. InceGaussian (IG) beams are the solutions of paraxial beams in an ellipticalcoordinate system. IG beams are the third calls of orthogonal Eigenstates and can probe the chirality structures of samples. Since IG modeshave a preferred symmetry (long axis versus short axis) this enables itto probe chirality better than Laguerre Gaussian or Hermite Gaussianmodes. This enables the propagation of more IG modes within anelliptical core fiber than Laguerre Gaussian modes or Hermite Gaussianmodes. Thus, IG modes can be used as a program signal for spectroscopyin the same manner that Laguerre Gaussian modes or Hermite Gaussianmodes are used. This enables the detection of types of materials andconcentration of materials using an IG mode probe signal.

The wave equation can be represented as a Helmholtz equation inCartesian coordinates as follows(∇² +k ²)E(x,y,z)=0E(x,y,z) is complex field amplitude which can be expressed in terms ofits slowly varying envelope and fast varying part in z-direction.E(x,y,z)=ψ(x,y,z)e ^(jkz)

A Paraxial Wave approximation may be determined by substituting ourassumption in the Helmholtz Equation.

${( {\nabla^{2}{+ k^{2}}} ){\psi.e^{jkz}}} = {{{0\frac{\delta^{2}\psi}{\delta\; x^{2}}} + \frac{\delta^{2}\psi}{\delta\; y^{2}} + \frac{\delta^{2}\psi}{\delta\; z^{2}} - {j\; 2k\frac{\delta\psi}{\delta\; z}}} = 0}$

We then make our slowly varying envelope approximation

$| \frac{\delta^{2}\psi}{\delta\; z^{2}} \middle| {\operatorname{<<}| \frac{\delta^{2}\psi}{\delta\; x^{2}} |} ,| \frac{\delta^{2}\psi}{\delta\; y^{2}} |,{ {2k} \middle| \frac{\delta\psi}{\delta\; z} \middle| {{\nabla_{t}^{2}\psi} + {j\; 2k\frac{\delta\psi}{\delta\; z}}}  = 0}$Which comprises a Paraxial wave equation.

The elliptical-cylindrical coordinate system may be define as shown inFIG. 82.

x = a cosh  ξcos η y = a sinh  ξsin η ξ ∈ (0, ∞), η ∈ (0, 2π)$a = {{{f(z)}\mspace{14mu}{where}\mspace{14mu}{f(z)}} = \frac{f_{0}{w(z)}}{w_{0}}}$

Curves of constant value of trace confocal ellipses as shown in FIG. 83.

${\frac{x^{2}}{a^{2}\mspace{14mu}\cosh^{2}\mspace{14mu}\xi} + \frac{y^{2}}{a^{2}\mspace{14mu}\sinh^{2}\mspace{14mu}\xi}} = {1\mspace{14mu}({Ellipse})}$

A constant value of η give confocal hyperbolas as shown in FIG. 84.

${\frac{x^{2}}{a^{2}\mspace{14mu}\cos^{2}\mspace{14mu}\eta} + \frac{y^{2}}{a^{2}\mspace{14mu}\sin^{2}\mspace{14mu}\eta}} = {1\mspace{14mu}({hyperbola})}$

An elliptical-cylindrical coordinate system may then be defined in thefollowing manner

$\nabla_{t}^{2}{= {{\frac{1}{h_{\xi}^{2}}\frac{\delta^{2}}{{\delta\xi}^{2}}} + {\frac{1}{h_{\eta}^{2}}\frac{\delta^{2}}{{\delta\eta}^{2}}}}}$Where h_(ξ), h_(η) are scale factors

$h_{\xi} = \sqrt{( \frac{\delta\; x}{\delta\xi} )^{2} + ( \frac{\delta\; y}{\delta\xi} )^{2}}$$h_{\eta} = \sqrt{( \frac{\delta\; x}{\delta\eta} )^{2} + ( \frac{\delta\; y}{\delta\eta} )^{2}}$$h_{\xi} = {h_{\eta} = {a\sqrt{{\sinh^{2}\mspace{14mu}\xi} + {\sin^{2}\mspace{14mu}\eta}}}}$$\nabla_{t}^{2}{= {\frac{1}{a^{2}\mspace{14mu}\sinh^{2}\mspace{14mu}\xi\mspace{14mu}\sin^{2}\mspace{14mu}\eta}( {\frac{\delta^{2}}{{\delta\xi}^{2}} + \frac{\delta^{2}}{{\delta\eta}^{2}}} )}}$

The solution to the paraxial wave equations may then be made inelliptical coordinates. Paraxial Wave Equation in Elliptic Cylindricalco-ordinates are defined as

${{\frac{1}{a^{2}( {\sinh^{2}\mspace{14mu}\xi\mspace{14mu}\sin^{2}\mspace{14mu}\eta} )}( {\frac{\delta^{2}\psi}{{\delta\xi}^{2}} + \frac{\delta^{2}\psi}{{\delta\eta}^{2}}} )} - {j\; 2k\frac{\delta\psi}{\delta\; z}}} = 0$

Assuming separable solution as modulated version of fundamental Gaussianbeam.

IG(r^(∼)) = E(ξ)N(η)  exp (jZ(z))ψ_(GB)(r^(∼))${{Where}\mspace{14mu}{\psi_{GB}( r^{\sim} )}} = {\frac{w_{0}}{w(z)}{\exp\lbrack {{- \frac{r^{2}}{w^{2}(z)}} + {j\frac{{kr}^{2}}{2{R(z)}}} - {j\;{\psi_{GS}(z)}}} \rbrack}}$E, N & Z are real functions. They have the same wave-fronts as ψ_(GB)but different intensity distribution.

Separated differential equations are defined as

${\frac{d^{2}E}{d\;\xi^{2}} - {{\epsilon sinh2\xi}\frac{dE}{d\;\xi}} - {( {a - {p\;{\epsilon cosh2\xi}}} )E}} = 0$${\frac{d^{2}N}{d\;\eta^{2}} - {{\epsilon sin2\eta}\frac{dN}{d\;\eta}} - ( {a - {p\;{\epsilon cos2\eta}}} )} = {{0 - {( \frac{z^{2} + z_{r}^{2}}{z_{r}} )\frac{dZ}{dz}}} = p}$Where a and p are separation constants

$\epsilon = \frac{f_{0}w_{0}}{w(z)}$

The even solutions for the Ince-Gaussian equations are

${{IG}_{pm}^{e}( {r^{\sim},\epsilon} )} = {\frac{{Cw}_{0}}{w(z)}{C_{p}^{m}( {{j\;\xi},\epsilon} )}{C_{p}^{m}( {\eta,\epsilon} )}\mspace{14mu}\exp\mspace{14mu}( {- \frac{r^{2}}{w^{2}(z)}} ) \times \exp\mspace{14mu} j\mspace{14mu}( {{kz} + \frac{{kr}^{2}}{2{R(z)}} - {( {p + 1} ){\psi_{GS}(z)}}} )}$The frequency of the even Ince Polynomials are illustrated in FIGS. 85Aand 85B and the modes and their phases are illustrated in FIG. 86.

The odd solutions for the Ince-Gaussian equations are

${{IG}_{pm}^{o}( {r^{\sim},\epsilon} )} = {\frac{{sw}_{0}}{w(z)}{S_{p}^{m}( {{j\;\xi},\epsilon} )}{S_{p}^{m}( {\eta,\epsilon} )}\mspace{14mu}\exp\mspace{14mu}( {- \frac{r^{2}}{w^{2}(z)}} ) \times \exp\; j\mspace{14mu}( {{kz} + \frac{{kr}^{2}}{2{R(z)}} - {( {p + 1} ){\psi_{GS}(z)}}} )}$The frequency of the odd Ince Polynomials are illustrated in FIGS. 87Aand 87B and the modes and their phases are illustrated in FIG. 88.

Thus, as previously discussed with respect to FIG. 59, by combining twoor more different types of spectroscopy techniques, various types ofdifferent parameters may be monitored and used for determining types andconcentrations of sample materials. The use of multiple types ofspectroscopic parameter analysis enables for more accurate and detailedanalysis of sample types and concentrations. Thus, any number ofspectroscopic techniques such as optical spectroscopy, infraredspectroscopy, Ramen spectroscopy, spontaneous Ramen spectroscopy,simulated Ramen spectroscopy, resonance Ramen spectroscopy, polarizedRamen spectroscopy, Ramen spectroscopy with optical vortices, THzspectroscopy, terahertz time domain spectroscopy, fluorescencespectroscopy, pump probe spectroscopy, OAM spectroscopy, or InceGaussian spectroscopy may be used in any number of various combinationsin order to provide better detection of sample types in concentrations.It should be realized that the types of spectroscopy discussed hereinare not limiting in any combination of spectroscopic techniques may beutilized in the analysis of sample materials.

Multi-Parameter Dual Comb Spectroscopy with OAM

One can perform precision spectroscopy with pairing optical frequencycombs which can improve the results. Referring now to FIG. 89, inbroadband frequency comb spectroscopy, the signal from an opticalfrequency comb is read by a conventional spectrometer, but in atechnique called dual-comb spectroscopy, that conventional spectrometer8902 and the instrument's limitations on speed and resolution areremoved. Instead, a second frequency comb 8904 takes on the workpreviously done by the spectrometer 8902. The result can be dramaticgains in data acquisition speed, spectral resolution and sensitivity.These techniques can be used in conjunction with multi-parameterspectroscopy 8906 leveraging wavelength, polarization and OAMspectroscopy 8908.

Optical Frequency Combs

An optical frequency comb 8904 is a spectrum consisting of hundreds ofthousands or millions of equally spaced, sharp lines-analogous having agreat many continuous-wave (CW) lasers simultaneously emitting atdifferent, equally spaced frequencies. Optical combs can be generated inmany ways; the most common method uses a phase-stabilized, mode-lockedultrashort-pulse laser. In the time domain, the laser produces a pulsetrain at a specific repetition rate, and with a specific, increasingadditional carrier-envelope phase with each successive pulse. When therepetition rate and carrier-envelope phase of the pulse train are bothstabilized against radio- or optical-frequency references, a Fouriertransformation of the laser's periodic pulse train shows a sharp,comb-like spectrum in the frequency domain

If the frequency comb is well stabilized and referenced to an absolutefrequency standard, such as an atomic clock, the comb spectrum becomesan extremely precise ruler for measuring optical frequencies. That rulerhas found applications in a wide variety of scientific problems:high-resolution frequency measurements of atomic, ionic or moleculartransitions to answer fundamental questions in physics; the detection oftiny amounts of Doppler shift; and other applications in attosecondphysics, ultrapure microwave generation, time-frequency transfer overlong distances, manipulation of atomic qubits, and many others.

One of the most active research areas for frequency combs is broadbandmolecular spectroscopy. The comb's millions of equally spaced, sharplines offer the opportunity to measure complex broadband molecularsignatures with high spectral resolution and sensitivity. Exploitingthose advantages, however, requires a spectrometer of sufficiently highresolution to resolve each individual comb line. One approach can be theuse of a spectrometer based on virtually imaged phased array (VIPA)disperser in combination with a diffraction grating; another commonscheme uses an analytical chemistry, the Michelson-type Fouriertransform spectrometer, and replaces the conventional broadband, usuallyincoherent light source with a frequency comb.

In this approach to frequency comb spectroscopy, the frequency combpulse train is split into interferometer arms, one of which includes amechanically scanned mirror, and the two pulse trains are sent throughthe sample to be analyzed. As the mirror is scanned, a series ofinterferograms is recorded with a single photo-receiver and a digitizer;Fourier transformation of the interferograms generates the spectrum,with a resolution determined by the maximum optical-path-lengthdifference of the interferometer.

The Dual-Comb Advantage

A key drawback of doing frequency comb spectroscopy with theMichelson-type setup described is speed: the scan rate of the setup,which is limited by the velocity of the scanning mirror, is commonlyonly on the order of Hz. Dual-comb spectroscopy eases this disadvantageby using a second frequency comb, rather than a moving mirror to supplythe delay time. The result can be a significant enhancement of thespectrometer's performance.

In the dual-comb setup, the pulse train forms a second comb, with aslightly different pulse repetition rate from the first, that isspatially combined with the train from the first comb. The combinedpulse train is passed through the sample to be analyzed, and detected bya photo-receiver. The result, in the time domain, is a repeated seriesof cross-correlation-like interferometric signals between the pulses,with a steadily increasing time difference based on the difference inrepetition rate between the two combs. The dual-comb interferograms thushave characteristics similar to those of a conventional Michelson-typeFourier transform spectrometer but because the dual-comb setup does notdepend on the mechanical motion of a mirror, its scanning rate isseveral orders of magnitude faster than that of the Michelson-typeinterferometer.

Another advantage of dual-comb spectroscopy emerges in the frequencydomain There, the mixing of the two optical combs, with slightlydifferent repetition rates, results in a third, down-convertedradio-frequency (RF) comb, with spacing between teeth equivalent to therepetition rate difference between the two optical combs. The sample'sresponse is thus encoded on this down-converted RF comb, and the beatmeasurement between the two optical combs generates a multi-heterodynesignal that can be recovered from the RF comb. In summary, thedown-converted comb inherits the coherence property of the opticalfrequency combs, enabling broadband spectroscopy with a high resolutionand accuracy with the speed and digital signal processing advantages ofRF heterodyne detection.

Small Wearable Device

Compact wearable optical devices based on Raman and NIR absorption todetect changes in physiological chemical levels in the body may also beimplemented. Along with the novel detection scheme, we are alsodeveloping the compact integrated electronic-photonic system (ultimatelyan integrated silicon-photonic system). A wearable device 9000 shouldinclude the following components as shown in FIG. 90. An MCU(microcontroller) 9002 controls overall operation of the wearable device9000. BLE (Bluetooth low energy) transmitter/receiver 9004 transmitssignals to and from the wearable device 9000. Trance-impedance amplifier(TIA) for internally amplifying signals. Drivers 9008 for drivingLED/lasers within the device 9000. High resolution ADC 9010 performsanalog to digital conversions. Flash memory 9012 stores data within thewearable device 9000. Real-time clock 9014 controls internal clockingoperations.

The major requirement is low quiescent current for every component,ability to enter deep sleep mode, low current consumption in operatingmode, low-frequency mode for real-time clock/low power operation, andsingle battery operation of the MCU (microcontroller) and BLE(blue-tooth low energy). MCU+BLE chipsets of 2013-2015 model yearprovide the following component options:

-   -   a) EFM32 (MCU Silicon Laboratories)+CC2541 (BLE chip Texas        Instruments) or BCM20732 (Broadcom), or    -   b) Single chip solution form Nordic Semiconductors NRF51822        which includes similar Cortex M0 core and BLE radio, BLE stack        is realized via underling Nordic proprietary OS (SoftDevice)        which occupies about 100 kB of chips memory.

Either of these two solutions is used in 90% of modern BLE wearabledevices. In the present case the preferred embodiment would be using thesingle chip solution from Nordic Semiconductor. Major characteristicsare:

1) External crystal for real-time clock,

2) 256 kb of memory (256 kb-100 kb (SoftDevice)=156 kB for the programand storage)

3) Sleep mode in 1 uA range

4) Support of all standard BLE profiles and adjustable radio power up to4 dBm.

It also supports ANT protocol which may be useful in future development.

The near infrared laser diode system provides approximately 30controllable channels between 1570 and 1600 nm, as well as an additionaltunable source between 1450 and 1600.

Similar portable devices may be used with respect to other embodimentsand uses described above, including the detection of proteins and foodspoilage or food organic bio-markers due to the various biochemicalmechanisms associated with food spoilage.

OAM Body-Imaging

Imaging through and parts of the body is critical for most biomedicaloptical technology. Past work has developed imaging and spectroscopy inselect transmission windows in the NIR where glucose and proteins havestrong absorptions while water has reduced absorption. Since opticaldetection of glucose or other chemical compounds will most likely needto be in a region free of strong absorptions from other molecules, andwill take place with OAM beams, imaging of the body tissues, brain, boneand skin with OAM may be used. Possible routes to investigate would bephase contrast and dark field imaging, ballistic transport of OAMthrough scattering media in the NIR and birefringent imaging. The diodelasers available for the wearable device can also be incorporated intothe NIR OAM imaging once a suitable detector is acquired and tested.Single channel detectors in the NIR are cheaper than 2D CCD arrays,however a scanning system and image construction software would beneeded when imaging with a single channel detector.

Potential Applications

A compact, handheld 3D spectrometer capable of simultaneouspolarization, wavelength, and OAM-spectroscopy operated in a broadelectromagnetic frequency range empowers consumers with tremendousamounts of useful information about such things as their food and airquality, household biological contaminants, medicinal identification,and health-related issues such as real-time information about dentalcaries. This section serves as an outline of some of the potentialapplications of 3D spectroscopy.

Food Industry

Food substances primarily consist of water, fat, proteins, andcarbohydrates. The molecular structure and concentration of foodsubstances govern their functional properties. Quantification of theseproperties dictates the quality of food in terms of minimum standards ofsuitability for human consumption or exposure which include chemical,biological, and microbial factors that may impact such parameters astheir shelf-life. Recent advances in industrialization of our foodsupply chains and changes in consumer eating habits have placed greaterdemand on the rapidity with which our food must be analyzed for safetyand quality. This demand requires appropriate analytical tools such asspectroscopy.

Food spectroscopy is a desirable analysis method because it requiresminimal or no sample preparation as well rapid, production-linemeasurements. Given the nature of spectroscopic analysis, multiple testsmay be done on the sample.

Outside the industrialized production line of our food supply, novelspectroscopic techniques could be employed at the level of individualconsumers. For example, an individual consumer may spectroscopicallymeasure the sugar concentration in his foods, overall food quality,ripeness, or identify a watermelon in the local grocery store as havingbeen spoiled using a pocket size laser-based spectrometer.

Nanoscale Material Development for Defense and National Security

Nanoscale material development for defense and national securitytechnologies generally necessitates the binding site to recognize thetarget of interest. Several spectroscopic techniques are currently basedon absorption, scattering, of light, such as electron absorption(UV-vis), photoluminescence (PL), infrared (IR) absorption, and Ramanscattering while more advanced techniques include single moleculespectroscopy, sum frequency generation, and luminescence up-conversion.These spectroscopy technologies aid in the fabrication process ofnanoscale material architectures employed as biological and chemicalsensors.

Chemical Industry

Optical spectroscopy of gas sensors is useful for a variety ofenvironmental, industrial, medical, scientific and householdapplications. The gas may be hazardous to human health, an atmosphericpollutant, or important in terms of its concentration for industrial ormedical purposes. Aside from triggering an alarm, it is frequentlydesirable to measure accurate, real-time concentrations of a particulartarget gas, which is often in a mixture of other gases. Consumers mayuse household units to monitor air for biological or chemical hazardssuch as airborne germs or carbon monoxide as well as surfactantcontaminations on and around children's play areas, toys, and bedrooms.Such units would be useful in school classrooms, business offices, andshopping malls to alert to facilities managers to potential healthhazards. Further units may be useful in various industrial settings,including for example, chemical and/or petrochemical facilities,including but not limited to, using near-infrared spectroscopy. Inaddition to improved environmental benefits of detecting variousfugitive emissions of gases, such detection presents various economicbenefits for industrial operators to fix fugitive emission sources forincreases in product recovery and abatement of governmental fines.

Pharmaceutical Industry

The manufacturing process of highly precise drug concentrations inpills, capsules and liquids requires strict real-time monitoring as maybe performed by optical spectroscopy technologies. Once produced anddistributed, consumers may readily identify pills and medication at homeusing an advanced, real-time spectroscopy technique integrated into ahandheld device.

Medical Industry

There is strong interest in developing more sophisticated optical biopsytechnologies that non-invasively detect disease. These technologies maybe driven by spectroscopy that may optically biopsy tissues without theneed to remove it from the patient's body. Such a technology may bedeveloped to produce a photonics finger imager for accurate prostatecheckups, breast mammograms, and other cancer-detection procedures. Apocket-sized dermatological spectrometer would give patients private,real-time information that may be combined with the patient's medicalrecord for discussion with medical professionals.

The use of small, handheld optical spectrometers can be integrated intoa patient's routine health maintenance schedule. An example is the earlydetection of chemicals associated with Alzheimer's disease andParkinson's by spectroscopic detection during routine eye exams.

Dentistry

Everyday personal dental care requires small tools and instruments suchas toothbrushes and dental floss. A toothbrush-size optical spectrometerwould be useful to detect the onset of small dental caries (tooth decayand cavities) and alert the consumer to schedule a visit to the familydentist who may have been sent tooth-specific information before thescheduled visit.

Biomedical Photonics

These technologies can be applied to, and not limited to, neuro-imagingapplications such as optical spectroscopy and correlation methods tomeasure oxygen and blood flow; the development of new microscopes forfunctional imaging to improve the quantitative interpretation ofmeasurement of brain activities and psychology using functionalnear-infrared spectroscopy; the development technologies such as diffusecorrelation spectroscopy to measure blood flow; and the development ofmulti-spectral optical imaging of cerebral hemoglobin.

It will be appreciated by those skilled in the art having the benefit ofthis disclosure that this system and method for the detection of thepresence of materials within a sample based on a unique signature. Itshould be understood that the drawings and detailed description hereinare to be regarded in an illustrative rather than a restrictive manner,and are not intended to be limiting to the particular forms and examplesdisclosed. On the contrary, included are any further modifications,changes, rearrangements, substitutions, alternatives, design choices,and embodiments apparent to those of ordinary skill in the art, withoutdeparting from the spirit and scope hereof, as defined by the followingclaims. Thus, it is intended that the following claims be interpreted toembrace all such further modifications, changes, rearrangements,substitutions, alternatives, design choices, and embodiments.

What is claimed is:
 1. An apparatus for detecting a material within asample, comprising: a light emitting unit for directing at least onelight beam through the sample, the at least one light beam having aunique Raman intensity signature associated therewith responsive topassing through the sample; a spontaneous Raman spectroscopic unit forreceiving the at least one light beam that has passed though the sampleand performing a spontaneous Raman spectroscopic analysis to detect afirst Raman intensity signature associated with the sample, wherein thefirst Raman intensity signature relates to molecular vibrations causedby the material in the sample; a simulated Raman spectroscopic unit forreceiving the at least one light beam that has passed through the sampleand performing a simulated Raman spectroscopic analysis to detect asecond Raman intensity signature associated with the sample, wherein thesecond Raman intensity signature relates to molecular vibrations causedby the material within the sample; a database including a plurality ofunique combinations of first Raman intensity signatures associated withspontaneous Raman spectroscopic analysis and second Raman intensitysignatures associated with simulated Raman spectroscopic analysis, eachof the plurality of unique combinations of the first and second Ramanintensity signatures associated with a particular material; and aprocessor for detecting the material within the sample responsive to acomparison of the plurality of unique combinations of the first andsecond Raman intensity signatures detected by the spontaneous Ramanspectroscopic unit and the simulated Raman spectroscopic unit with theplurality of unique combinations of the first and second Raman intensitysignatures within the database and a determination of a matching uniquecombination of the first and second Raman intensity signatures withinthe database, wherein spontaneous Raman intensity is linearly dependenton an incident intensity and simulated Raman intensity is nonlinearlydependent on the incident intensity.
 2. The apparatus of claim 1,wherein the light emitting beam further applies an orbital angularmomentum to the at least one light beam that is directed through thesample.
 3. The apparatus of claim 2 further comprises an OAMspectroscopic unit for receiving the at least one light beam that haspassed though the sample and performing an orbital angular momentum(OAM) spectroscopic analysis to detect a rotational signature associatedwith the sample.
 4. The apparatus of claim 3, wherein the databasefurther includes a plurality of unique combinations of first Ramanintensity signatures associated with spontaneous Raman spectroscopicanalysis, second Raman intensity signatures associated with simulatedRaman spectroscopic analysis and rotational signatures, each of theplurality of unique combinations of first and second Raman intensitysignatures and rotational signatures associated with a particularmaterial.
 5. The apparatus of claim 4, wherein the processor detects thematerial within the sample responsive to a comparison of the pluralityof unique combinations of the first and the second Raman intensitysignatures and the rotational signature detected by the spontaneousRaman spectroscopic unit, the simulated Raman spectroscopic unit and theOAM spectroscopic unit with the plurality of unique combinations of thefirst and the second Raman intensity signatures and the rotationalsignatures within the database and a determination of a matching uniquecombination of the first and the second Raman intensity and therotational signatures within the database.
 6. An apparatus for detectinga material within a sample, comprising: a light emitting unit fordirecting at least one light beam having an orbital angular momentum andenergy mode applied thereto through the sample, the at least one lightbeam having a unique vibrational and rotational signature combinationassociated therewith responsive to passing through the sample; an OAMspectroscopic unit for receiving the at least one light beam that haspassed though the sample and performing an orbital angular momentum(OAM) spectroscopic analysis to detect a rotational signature associatedwith the sample; a resonance Raman spectroscopic unit for receiving theat least one light beam that has passed through the sample andperforming a resonance Raman spectroscopic analysis to detect avibrational signature associated with the sample, wherein thevibrational signature comprises vibrational modes caused by the materialwithin the sample that match the energy mode associated with the atleast one light beam; a database including a plurality of uniquecombinations of vibrational and rotational signatures, each of theplurality of unique combinations of vibrational and rotationalsignatures associated with a particular material; and a processor fordetecting the material within the sample responsive to a comparison ofthe plurality of unique combinations of the vibrational and therotational signatures detected by the OAM spectroscopic unit and theresonance Raman spectroscopic unit with the plurality of uniquecombinations of the vibrational and rotational signatures within thedatabase and a determination of a matching unique combination of thevibrational and rotational signatures within the database, whereinidentification of the matching unique combination of the vibrational androtational signatures enables detection of the material not detectableusing either the vibrational signature or the rotational signaturealone.
 7. The apparatus of claim 6, wherein intensities of thevibrational modes are proportional to a 6^(th) power of a frequency. 8.The apparatus of claim 6, wherein the unique combination of vibrationaland rotational signatures provides sensitive discrimination of closemolecular species.
 9. An apparatus for detecting a material within asample, comprising: a light emitting unit for directing at least onelight beam having an orbital angular momentum applied thereto toward thesample, the at least one light beam having a unique vibrational androtational signature combination associated therewith responsive topassing through the sample; a polarizer for applying at least a firstpolarization and a second polarization to the at least one light beam;an OAM spectroscopic unit for receiving the at least one light beam thathas passed though the sample and performing an orbital angular momentum(OAM) spectroscopic analysis to detect a rotational signature associatedwith the sample; a polarized Raman spectroscopic unit for receiving theat least one light beam having either the first polarization or thesecond polarization applied thereto that has passed through the sampleand performing a polarized Raman spectroscopic analysis to detect avibrational signature associated with the sample, wherein thevibrational signature comprises a unique ratio of intensities based onapplication of the first polarization and the second polarization to theat least one light beam caused by the material within the sample; adatabase including a plurality of unique combinations of vibrational androtational signatures, each of the plurality of unique combinations ofthe vibrational and the rotational signatures associated with aparticular material; and a processor for detecting the material withinthe sample responsive to a comparison of the plurality of uniquecombinations of the vibrational and the rotational signatures detectedby the OAM spectroscopic unit and the polarized Raman spectroscopic unitwith the plurality of unique combinations of the vibrational and therotational signatures within the database and a determination of amatching unique combination of the vibrational and the rotationalsignatures within the database, wherein identification of the matchingunique combination of the vibration and the rotational signaturesenables detection of the material not detectable using either thevibrational signature or the rotational signature alone.
 10. Theapparatus of claim 9, wherein the polarizer is located between the lightemitting unit and the sample.
 11. The apparatus of claim 9, wherein thepolarizer is located between the sample and the OAM spectroscopic unitand polarized Raman spectroscopic unit.
 12. The apparatus of claim 9,wherein polarized Raman spectroscopic unit further receives the at leastone light beam having no polarization applied thereto that has passedthrough the sample and performing a non-polarized Raman spectroscopicanalysis to detect a vibrational signature associated with the sample,wherein the vibrational signature comprises a unique ratio ofintensities based on application of the first polarization, the secondpolarization and the non-polarization applied to the at least one lightbeam caused by the material within the sample.
 13. An apparatus fordetecting a material within a sample, comprising: a light emitting unitfor directing a pump beam and a probe beam, the probe beam having anorbital angular momentum applied thereto through the sample, the probebeam having a unique vibrational and rotational signature combinationassociated therewith responsive to passing through the sample; an OAMspectroscopic unit for receiving the probe beam that has passed thoughthe sample and performing an orbital angular momentum (OAM)spectroscopic analysis to detect a rotational signature associated withthe sample; a pump probe spectroscopic unit for receiving the probe beamthat has passed through the sample and performing a pump probespectroscopic analysis to detect a molecular signature associated withthe sample, wherein the molecular signature relates to ultrafastmolecular phenomenon relating to transient properties of moleculescaused by the material within the sample; a database including aplurality of unique combinations of molecular and rotational signatures,each of the plurality of unique combinations of the molecular androtational signatures associated with a particular material; and aprocessor for detecting the material within the sample responsive to acomparison of the plurality of unique combinations of the molecular andthe rotational signatures detected by the OAM spectroscopic unit and thepump probe spectroscopic unit with the plurality of unique combinationsof the molecular and the rotational signatures within the database and adetermination of a matching unique combination of molecular androtational signatures within the database, wherein identification of thematching unique combination of the vibrational and rotational signaturesenables detection of the material not detectable using either themolecular signature or the rotational signature alone.
 14. The system ofclaim 13, wherein the light emitting unit further comprises: a laser forgenerating a light beam; a beam splitter for splitting the light beaminto a first light beam and a second light beam; pump generationcircuitry for generating the pump beam responsive to the first lightbeam for exciting molecules within the sample; and probe generationcircuitry for generating the probe beam responsive to the second lightbeam for detecting the molecular signature.
 15. The apparatus of claim14, wherein the pump generation circuitry generates the pump beam at afirst frequency and the probe generation circuitry generates the probebeam at a second frequency, further wherein scattering intensities areenhanced by differences between the first frequency and the secondfrequency.
 16. The apparatus of claim 14, wherein the pump generationcircuitry generates the pump beam at a first frequency that inducesRaman emissions and the probe generation circuitry generates the probebeam at a second frequency that helps detect Raman modes.